Methods and apparatus to detect and annotate backedges in a dataflow graph

ABSTRACT

Disclosed examples to detect and annotate backedges in data-flow graphs include: a characteristic detector to store a node characteristic identifier in memory in association with a first node of a dataflow graph; a characteristic comparator to compare the node characteristic identifier with a reference criterion; and a backedge identifier generator to generate a backedge identifier indicative of a backedge between the first node and a second node of the dataflow graph based on the comparison, the memory to store the backedge identifier in association with a connection arc between the first and second nodes.

STATEMENT REGARDING FEDERALLY SPONSERED RESEARCH AND DEVELOPMENT

This invention was made with Government support under subcontract numberB620873 awarded by the Department of Energy. The Government has certainrights in this invention.

FIELD OF THE DISCLOSURE

This disclosure relates generally to programmable computing devices andmore particularly, to methods and apparatus to detect and annotatebackedges in a dataflow graph.

BACKGROUND

A processor, or set of processors, execute(s) instructions from aninstruction set (e.g., an instruction set architecture (ISA)). Theinstruction set is the part of the computer architecture related toprogramming, and generally includes native data types, instructions,register architecture, addressing modes, memory architecture, interruptand exception handling, and external input and output (I/O) information.Instructions may be macro-instructions provided to a processor forexecution, and/or may be micro-instructions generated by a processorbased on decoding macro-instructions.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts an example backedge detector and an example bufferinserter implemented in accordance with teachings of this disclosure todetect and remove backedges from dataflow graphs and insert buffers inthe dataflow graphs.

FIGS. 2A-2C depict an example dataflow graph including a back-pressurednoncritical path and a critical path including a backedge.

FIGS. 3A-3C depict an example dataflow graph including buffers insertedin the noncritical path of FIGS. 2A-2C.

FIG. 4 illustrates example source code in the C programming language,corresponding assembly code, and a corresponding dataflow graph of theoperations in the assembly code.

FIG. 5 is an example compiling and optimization workflow of the compilerof FIG. 1.

FIG. 6 is a dataflow graph showing backedges annotated using aDepth-First Search technique.

FIG. 7 depicts example pseudocode representing machine-readableinstructions that may be executed by a processor to implement aDepth-First Search to detect and annotate backedges in a dataflow graph.

FIG. 8 depicts example pseudocode representing machine-readableinstructions that may be executed by a processor to implement aBreadth-First Search to detect and annotate backedges in a dataflowgraph.

FIG. 9 depicts example pseudocode representing machine-readableinstructions that may be implemented by a processor to implementpost-order traversal and dominator analyses to detect and annotatebackedges in dataflow graphs.

FIG. 10 depicts an example workflow of the compiler of FIG. 1 in whichexamples disclosed herein may be implemented to latency-balance dataflowgraphs for execution on coarse-grain reconfigurable architecture (CGRA)devices.

FIG. 11 is a flowchart representative of example machine-readableinstructions which may be executed to implement the example compiler ofFIG. 1.

FIG. 12 is a flowchart representative of example machine-readableinstructions which may be executed to implement the example backedgedetector of FIG. 1 to detect and annotate backedges from dataflowgraphs.

FIG. 13 is a flowchart representative of example machine-readableinstructions which may be executed to implement the example bufferinserter of FIG. 1 to insert buffers in dataflow graphs.

FIG. 14 is a block diagram of an example processing platform structuredto execute the instructions of FIGS. 11-13 to implement the examplecompiler of FIG. 1, the example backedge detector of FIG. 1, and/or theexample buffer inserter of FIG. 1.

FIG. 15 depicts an example array of processing elements (PEs) of a CGRAdevice.

FIG. 16 depicts an enlarged view of the example array of PEs of FIG. 15.

FIG. 17 is an example comparative bar graph comparing storage boxes usedby an automatic buffer insertion process implemented in accordance withteachings of this disclosure with and without throughput as aconstraint.

FIG. 18 is an example comparative bar graph comparing performance of apractical dataflow graph to a dataflow graph with unpractically deep 128depth buffers for all edges when an automatic buffer insertion processis implemented in accordance with teachings of this disclosure with andwithout throughput as a constraint.

The figures are not to scale. Instead, the thickness of the layers orregions may be enlarged in the drawings. In general, the same referencenumbers will be used throughout the drawing(s) and accompanying writtendescription to refer to the same or like parts.

Descriptors “first,” “second,” “third,” etc. are used herein whenidentifying multiple elements or components which may be referred toseparately. Unless otherwise specified or understood based on theircontext of use, such descriptors are not intended to impute any meaningof priority, physical order or arrangement in a list, or ordering intime but are merely used as labels for referring to multiple elements orcomponents separately for ease of understanding the disclosed examples.In some examples, the descriptor “first” may be used to refer to anelement in the detailed description, while the same element may bereferred to in a claim with a different descriptor such as “second” or“third.” In such instances, it should be understood that suchdescriptors are used merely for ease of referencing multiple elements orcomponents.

DETAILED DESCRIPTION

Examples disclosed herein latency-balance a dataflow graph (e.g., cyclicdataflow graphs and/or acyclic dataflow graphs) by injecting buffersinto the dataflow graph. As used herein, a dataflow graph (DFG) is agraphical representation of a computer program. A cyclic DFG is ageneral dataflow graph that contains cycles or loops to representlooping or iterative operations in a computer program. An acyclic DFG isa general dataflow graph that does not contain cycles or loops. DFGs maybe produced by a compiler, a software framework, or written by hand.Examples disclosed herein are described in connection with DFGsgenerated for an example type of computer architecture known as acoarse-grained reconfigurable architecture (CGRA). CGRA-based devicesinclude thousands of tiny reconfigurable processing elements (PEs)arranged or formed on a spatial grid and connected via on-chipreconfigurable network connections. A particular example of a CGRA is aconfigurable spatial accelerator (CSA) architecture developed by IntelCorporation of Santa Clara, Calif., USA. Examples disclosed herein maybe used to process dataflow graphs targeted for execution on a CSAarchitecture, targeted for execution any other type of CGRA, and/ortargeted for execution on any other type of machine architecture.

A CSA target device can be programmed by writing CSA-specific assemblyinstructions (e.g., using an instruction set architecture (ISA)).Examples disclosed herein may be implemented in connection with acompiler for CSA target devices that can be used to compile high-levellanguages such as the C programming language, the C++ programminglanguage, the FORTRAN programming language, etc. into CSA-specific LLVMIR (Intermediate Representation) language. The term LLVM is not anacronym but is a term in itself that refers to a manner of representingcode for use in compiler-based analysis and optimization. LLVM coderepresentations are defined by the LLVM Foundation. However, examplesdisclosed herein may be implemented in connection with a general LLVM IRor any other suitable type of compiler IR for any other type of machineor architecture in addition to or instead of a machine-specific LLVM IRsuch as CSA-specific LLVM IR. The compiler can optimize and compilecompiler IR code or LLVM IR code into a CSA assembly which is then usedto create a DFG. During such transformation, the compiler can propagateor hold high-level program-specific information as well asprogrammer-specified hints to the assembly level such as loopmembership, performance critical operations, throughput, etc. which canbe used by subsequent tools for preparing the program for loading on atarget device. For example, such subsequent tools can use the dataflowrepresentation of the DFG to optimize the DFG by fusing suitableoperations together, balancing available buffering with latency inaccordance with teachings of this disclosure, mapping operations totarget hardware, and placing and routing operations and storage in thetarget hardware. A high-level workflow representation of a compiler forCSA devices and/or any other type of CGRA devices is shown in Table 1below.

TABLE 1 Compiler Workflow Compiler generates LLVM IR from C/C++/Fortrancode Compiler generates Assembly code Operation Elaboration and FusionBuffer Insertion Place and Route Binary Configuration Generation

While Table 1 above shows an example manner of organizing a compilerworkflow, the example stages depicted in Table 1 can be reordered, oneor more of the stages can be run multiple times in any sequence, one ormore of the stages can be omitted, and/or one or more other stages canbe inserted. Example latency-balancing techniques disclosed herein maybe implemented in the Buffer Insertion phase of a compiler shown inTable 1 above by analyzing DFGs generated by the Operation Elaborationand Fusion phase. A DFG is formed using interconnected nodes in whicheach node represents an operation (e.g., a compute operation, a memoryoperation, a control operation, etc.) and each interconnection or arcrepresents a producer-consumer dataflow relationship (e.g., aninput-output dependency) between two operations. For example, for twointerconnected nodes forming an input-output dependency, a first node isa producer/source node and a second node is a consumer/destination/sinknode. The producer/source node is the dominator node that performs aproducer/source operation to produce an output that is consumed as inputin the consumer/destination/sink node to perform aconsumer/destination/sink operation.

A DFG defines nodes of operations and their interconnections and is usedto configure PEs of CGRA devices. Different PEs of a CGRA device may bestructured for different types of operations. For example, some PEs maybe structured to perform integer arithmetic operations, some PEs may bestructured to perform floating point arithmetic operations, some PEs maybe structured to perform communication operations, and some PEs may bestructured as in-fabric storage to store data. In the above example,multiple nodes of a DFG may be configured in a single PE or may beconfigured in different PEs depending on the types of operations of themultiple nodes. In examples disclosed herein, in-fabric storage PEs,also referred to as storage boxes, are memory (e.g., random accessmemory (RAM), static RAM (SRAM), dynamic RAM (DRAM), etc.) used toimplement buffers for use in latency-balancing DFGs. Additionally oralternatively, storage boxes can be used for other functionalities suchas addressable memory. A buffer may be of any size so long as it doesnot exceed the capacity of the storage box from which it is allocated.The number of buffers available in a CGRA device is based on the numberof storage boxes in the CGRA device because the buffers are allocatedfrom the storage boxes.

In examples disclosed herein, a DFG includes one or more cycles or loopsbetween start nodes and corresponding end nodes. For a corresponding setof start and end nodes there may be multiple paths between the two. Eachpath has a corresponding latency which is the duration of performingtheir respective operations between the start node and the end node. Inthose multiple paths is a critical path that is attributable to thelongest latency between the start and end nodes relative to latencies ofthe other path(s) between the start and end nodes. The long latency ofthe critical path is due to the critical path having more operationnodes and/or longer-latency nodes than the other paths.Latency-balancing by buffering means adding storage elements (e.g.,buffers) and/or processing elements on interconnecting arcs betweennodes along a path between start and end nodes to make the overallstorage in that path produce a path latency tolerance that is similar orequal to a latency of the critical path (e.g., a critical path latency).Contrary to conventional design principals of reducing latency inprograms to increase performance, latency-balancing techniques disclosedherein add latency to paths to increase performance. As described ingreater detail below, increasing a latency of one or more noncriticalpaths to be similar or equal to the critical path latency balances thelatency between the noncritical and critical paths which increases thedata processing throughput of the noncritical and critical paths.

Example latency-balancing techniques disclosed herein include twophases, namely an example backedge detection phase and an example bufferinsertion phase. As used herein, a backedge in a DFG is aninterconnecting arc between a child node or operation and a parent nodeor operation. A backedge transfers execution control from the child nodeto the parent node and denotes a cyclic dependency among operations inthe DFG between the child and parent nodes. That is, operations or nodesform a cyclic dependency when execution of a node (e.g., an ancestornode or parent node) is dependent on output(s) from one or moresuccessor nodes (e.g., one or more child nodes or descendent nodes). Inexamples disclosed herein, detection and removal of backedges isperformed before buffer insertion. As such, the example backedgedetection phase involves: (a) analyzing a DFG to detect backedges thatform loops in a program between loop start nodes and loop end nodes, and(b) annotating the backedges in the DFG. The example buffer insertionphase involves removing the annotated backedges and analyzing theremaining paths in the DFG to determine suitable quantities of buffersto insert in noncritical paths between loop start and loop end nodes toincrease data throughputs of those noncritical and critical pathsbetween loop start and loop end nodes.

FIG. 1 depicts an example compiler 100 including an example backedgedetector 102 and an example buffer inserter 104 implemented inaccordance with teachings of this disclosure to latency-balance paths inthe DFGs by detecting and removing backedges from the DFGs and insertingbuffers in the DFGs. Although not shown, the example compiler 100includes other components such as components to implement the processesof the compiler workflow shown in Table 1 above, and the examplecompiler workflow described below in connection with FIG. 10, and/orother components not reflected in those example compiler workflows. Forpurposes of this disclosure, such other components are omitted from theexample of FIG. 1. However, it should be understood that a compilerimplemented in accordance with teachings of this disclosure couldinclude one or more of such omitted components. Examples of featuresthat could be implemented in the compiler 100 are described below inconnection with FIGS. 5 and 10. In addition, although the backedgedetector 102 and the buffer inserter 104 are shown as part of theexample compiler 100, in other examples, the backedge detector 102 andthe buffer inserter 104 may be implemented separate from the compiler100. For example, the backedge detector 102 and the buffer inserter 104may be implemented in later tools to optimize DFGs after processes bythe compiler 100 are completed.

In the illustrated example of FIG. 1, the example backedge detector 102includes an example characteristic detector 106, an examplecharacteristic comparator 108, and an example backedge identifiergenerator 110. Also in the illustrated example of FIG. 1, the examplebuffer inserter 104 includes an example backedge filter 112, an examplelatency calculator 114, an example latency comparator 116, an examplebuffer allocator 118, and an example delay generator 120. In the exampleof FIG. 1, the backedge detector 102 and the buffer inserter 104 are incircuit with example memory 124. The example memory 124 may beimplemented by one or more volatile memory devices (e.g., dynamic randomaccess memory (DRAM), static random access memory (SRAM), cache memory,etc.) and or one or more nonvolatile memory devices (e.g., flash memory,NAND flash memory, 3D NAND flash memory, NOR flash memory, etc.). In theexample of FIG. 1, the backedge detector 102 uses the memory 124 tostore information representative of backedges detected in DFGs, and thebuffer inserter 104 accesses the backedge information from the memory124 for use in a buffer insertion process to insert buffers into DFGs.

In the example of FIG. 1, the backedge detector 102 obtains an exampleinput DFG 126. The example input DFG 126 is generated by the compiler100 based on source code in at least one of a high-level programminglanguage (e.g., the C programming language, the C++ programminglanguage, the FORTRAN programming language, etc.) or a low-levelprogramming language such as the assembly programming language. Aspersons skilled in the art would readily understand, a high-levelprogramming language is more similar to a spoken or written language,whereas a low-level programming language is more similar to machinecode. The example backedge detector 102 analyzes the input DFG 126 forthe presence of backedges, and annotates detected backedges in the inputDFG 126. In the example of FIG. 1, the input DFG 126 includes 5 nodes oroperations labeled as example operations o1-o6. The example operationso1-o6 may be arithmetic operations, communication operations, bitmanipulation operations, storage operations, and/or any other types ofoperations for which PEs are available to perform in a target devicethat is to execute the DFG. The example input DFG 126 includes anoncritical path (e.g., an example noncritical path 202 of FIG. 2)formed by operations o1, o6, and o5. The example input DFG 126 alsoincludes a critical path (e.g., an example critical path 204 of FIG. 2)formed by operations o1-o5. The path of operations o1-o5 is regarded asthe critical path because it has a longer latency to completion (e.g.,reaching operation o5) than the noncritical path of operations o1, o6,and o5. The example input DFG 126 also includes an example backedge 128that returns execution control from operation o5 to operation o2 in thecritical path. Although only a single backedge 128 is shown in theillustrated example of FIG. 1, examples disclosed herein may be used toprocess input DFGs having multiple backedges. In addition, although theexample backedge 128 is shown in connection with the critical path,examples disclosed herein may be implemented in connection withbackedges along noncritical paths.

In the example of FIG. 1, the buffer inserter 104 removes backedges fromDFGs and inserts buffers into the DFGs to latency-balance noncriticalpaths and critical paths of operations between source nodes (e.g., thesource node of operation o1 in FIG. 1) and sink nodes (e.g., the sourcenode of operation o5 in FIG. 1). For example, as shown in FIG. 1, thebuffer inserter 104 removes annotated backedges from the input DFG 126to generate an acyclic DFG represented by an example intermediate DFG130. The example buffer inserter 104 also labels the source node of theremoved backedge as a loop end node (e.g., the fifth node o5) and labelsthe sink node of the removed backedge as a loop start node (e.g., thesecond node o2) in the intermediate DFG 130. The buffer inserter 104then uses the intermediate DFG 130 to perform buffer insertion analysesin accordance with examples disclosed herein, and inserts two examplebuffers 136, 138 in the example input DFG 126 based on the bufferinsertion analyses to generate an example output DFG 132. As shown inthe example of FIG. 1, the output DFG 132 also includes the backedge128, as in the input DFG 126. Uses of the example buffers 136, 138 tolatency-balance the output DFG 132 are described below in connectionwith FIGS. 3A-3C. When the DFG 132 is loaded on a target device, theexample buffers 136, 138 are implemented by storage PEs in the array ofPEs of the target device. In the example of FIG. 1, a target device isshown as an example course-grain reconfigurable architecture (CGRA)device 142 which includes an array of PEs interconnected by a network.The example output DFG 132 is used to configure the PEs in the CGRAdevice 142 so that the CGRA device 142 is structured to implement theprocess defined by the output DFG 132. Ones of the nodes o1-o6 may beexecuted by a same PE or different PEs of the CGRA device 142. Forexample, the second node o2 may be executed by a first one of the PEs,and the third node o3 may be executed by a second one of the PEs.Alternatively, the second node o2 and the third node o3 may be executedby the same PE.

Turning to the example backedge detector 102, to improve performance ofthe input DFG 126 which is targeted to be executed by the CGRA device142, the backedge detector 102 analyzes the input DFG 126 to detectbackedges. The example backedge detector 102 may perform such analysesusing a depth-first search (DFS) technique, a breadth-first search (BFS)technique, a technique that combines Johnson's algorithm with DFS, apost-order traversal and dominator analysis technique, a manual backedgeannotation technique, or any other suitable technique. Example backedgeanalysis techniques are described in greater detail below in connectionwith FIGS. 6-9.

In some backedge detection examples, the backedge detector 102 analyzescharacteristics of the nodes o1-o6 and compares such characteristics toreference criteria to determine which nodes are connected to backedges.The example backedge detector 102 is provided with the characteristicdetector 106 to store node characteristic identifiers in the memory 124in association with nodes of the input DFG 126. For example, thecharacteristic detector 106 can store a node characteristic identifierin the memory 124 in association with the second node o2 of the inputDFG 126. As defined herein, a node characteristic identifier representsinformation about an execution status of a node or a hierarchicallocation of a node relative to other nodes in a DFG. Example nodecharacteristic identifiers are described below in connection with FIGS.7-9.

The example backedge detector 102 is provided with the examplecharacteristic comparator 108 to compare node characteristic identifierswith reference criteria. As defined herein, a reference criterionrepresents a value to which a node characteristic identifier is comparedto determine whether a node corresponding to the node characteristicidentifier is connected to a backedge. Example reference criteria aredescribed below in connection with FIGS. 7-9. The example backedgedetector 102 is provided with the example backedge identifier generator110 to generate a backedge identifier indicative of a backedge betweenthe second node o2 and the fifth node o5 of the DFG 126 based on thecomparison performed by the characteristic comparator 108. The examplebackedge identifier generator 110 annotates a backedge by storing thebackedge identifier in the memory 124 in association with a connectionarc between the first and second nodes (e.g., the connection arc betweenthe second node o2 and the fifth node o5). For example, the memory 124may store a data structure or table of records or entries correspondingto connection arcs between different ones of the nodes o1-o6 of the DFG126. Additionally or alternatively, the memory 124 may store assemblycode of the DFG 126 in which the backedge identifier generator 110inserts backedge mnemonics as backedge identifiers at locations in theassembly code corresponding to connection arcs of the DFG 126 identifiedas being backedges. In any case, the memory 124 may store a bit value, astring value, a mnemonic, or any other value as a backedge identifier torepresent a backedge in records or entries or as lines of codecorresponding to ones of the connection arcs identified as backedges. Inthe example of FIG. 1, the connection arc between the second node o2 andthe fifth node o5 is annotated in the memory 124 as the backedge 128. Anexample backedge annotation identifier that may be generated by thebackedge identifier generator 110 in assembly code is described below inconnection with FIG. 4 as a backedge attribute “.attrib backedge” 408.In such examples, the backedge identifier generator 110 can insert suchbackedge attributes in assembly code of the DFG 126 in the memory 124 asbackedge identifiers to represent where backedges exist in the assemblycode. However, examples disclosed herein are not limited to anyparticular manner of annotating backedges in the memory 124. Instead,examples disclosed herein may employ any suitable manner of annotatingan edge by the backedge detector 102 that adds an attribute to aninterconnecting arc's name corresponding to a detected backedge.Annotating an edge with a backedge attribute by addingbackedge-identifying text before the edge's declaration provides a hintregarding that interconnecting arc forming a backedge which can then beused by the buffer inserter 104 to optimize/handle backedges (e.g.,remove backedges) in accordance with examples disclosed herein toperform buffer insertion. In some examples, the backedge detector 102may perform a verification process to confirm the DFG 126 would beacyclic if all annotated backedges were removed before performing abuffer insertion process. In this manner, if the backedge detector 102determines that an acyclic DFG would not be produced, the backedgedetector 102 can re-analyze the DFG 126 for additional backedges.

After the backedge identifier generator 110 annotates the backedges ofthe input DFG 126, the example buffer inserter 104 accesses the backedgeidentifiers stored in the memory 124 to perform a buffer insertionprocess by removing backedges from the input DFG 126 and insertingbuffers to generate the output DFG 132. The example buffer inserter 104includes the example backedge filter 112 to remove backedges betweennodes to generate an acyclic DFG as represented by the intermediate DFG130. For example, the backedge filter 112 accesses a backedge identifierfrom the memory 124 identifying the connection arc between the secondnode o2 and the fifth node o5 as being a backedge 128. Based on thebackedge identifier, the backedge filter 112 removes the backedge 128between the second node o2 and the fifth node o5 of the input DFG 126.Thus, although the example input DFG 126 is cyclic because it includes acycle formed by the backedge 128, example latency-balancing techniquesdisclosed herein detect and remove backedges such as the backedge 128 toremove cycles which creates acyclic DFGs (e.g., the intermediate DFG130) before inserting buffers. In addition, although the examplebackedge 128 is removed from a critical path of the DFG 126,implementations of examples disclosed herein may annotate and/or removebackedges from critical paths and/or noncritical paths to perform bufferinsertion. That is, examples disclosed herein may be used to make a DFGacyclic by annotating and removing all backedges regardless of whetherthose backedges occur on critical paths and/or noncritical paths of theDFG.

The buffer inserter 104 is provided with the example latency calculator114 to determine critical path latencies of critical paths of DFGs. Forexample, the latency calculator 114 can determine a critical pathlatency of the critical path of the intermediate DFG 130 formed by thenodes o1-o5. The example latency calculator 114 also determines thenoncritical path latency of the noncritical path formed by the nodes o1,o6, o5. In the example of FIG. 1, the path formed by the nodes o1-o5 isthe critical path of the intermediate DFG 130 because it has a longerlatency to completion (e.g., terminating at the fifth node o5) relativeto the noncritical path formed by node o1, o6, o5 (e.g., alsoterminating at the fifth node o5).

The buffer inserter 104 is provided with the example latency comparator116 to compare the critical path latency to a latency sum of a bufferlatency and the noncritical path latency. In examples disclosed herein,a buffer latency is an amount of latency introduced into a path of a DFGfor each inserted buffer (e.g., one of the buffers 136, 138 of FIG. 1).The latency comparator 116 analyzes the latency sum of a buffer latencyand the noncritical path latency to determine whether adding a buffer(e.g., one of the buffers 136, 138 of FIG. 1) to the noncritical pathwill exceed the critical path latency of the intermediate DFG 130. Thatis, examples disclosed herein latency-balance paths of the DFG so that anoncritical path latency is equal to or substantially similar to, butnot greater than, the critical path latency of the DFG. In otherexamples, techniques disclosed herein may be used to insert a number ofbuffers in the noncritical path that would result in increasing thelatency of the noncritical path to exceed the critical path latency. Insuch other examples, the noncritical path becomes the new critical path,and the previous critical path becomes a noncritical path. In thismanner, critical and noncritical paths may be interchanged throughpath-latency adjustments to produce a DFG with a desired target datathroughput.

The buffer inserter 104 is provided with the example buffer allocator118 to insert one or more buffers in noncritical paths of DFGs based onbuffer insertion analyses of acyclic, intermediate DFGs (e.g., theintermediate DFG 130). For example, the buffer allocator 118 inserts thebuffer 136 in the noncritical path (e.g., nodes o1, o6, o5) of the inputDFG 126 when the comparator determines that the latency sum (e.g., thesum of the buffer latency and the noncritical path latency) is less thanthe critical path latency of the critical path of the intermediate DFG130. In examples disclosed herein, a capacity sum of a path or edge isat least as large as its latency sum because the capacity should belarge enough to tolerate the latency (or buffers) in that path. As such,when the capacity sum of the noncritical path is less than the latencyof the critical path, examples disclosed herein can add more capacity tothe noncritical path so that the capacity of the noncritical path isproportional to the latency of the critical path. In such examples, theproportion is equal to the desired throughput of the part of the DFGunder analysis. For examples in which a maximum throughput of one (e.g.,one data token per cycle) is desired, the capacity sum of thenoncritical path is made equal to the latency of the critical path.After inserting the buffer 136, the latency calculator updates thenoncritical path latency to be based on the critical path being formedby nodes o1, o6, o5 and the inserted buffer 136. Subsequently, thebuffer inserter 104 can use the latency comparator 116 to determinewhether to insert another buffer. For example, the latency comparator115 can compare the critical path latency of the critical path (nodeso1-o5) to a latency sum of a buffer latency and the updated noncriticalpath latency. If the example latency comparator 116 determines that thelatency sum does not exceed the critical path latency, the bufferallocator 118 inserts another buffer 138 in the noncritical path of theinput DFG 126. In this manner, the buffer inserter 104 can use thelatency calculator 114 and the latency comparator 116 to determine wheninserting another buffer into the noncritical path would exceed thecritical path latency of the intermediate DFG 130. When the examplelatency comparator 116 determines that the critical path latency wouldbe exceeded by inserting another buffer in the noncritical path, thebuffer inserter 104 determines that no further buffer should be insertedinto the noncritical path of the input DFG 126. Alternatively asdescribed above, in some examples, the latency of a noncritical path isintentionally made to exceed a latency of a critical path throughinserting one or more buffers in the noncritical path. In such examples,the previous noncritical path becomes the current critical path, and theprevious critical path becomes a noncritical path. This may be done tofacilitate latency-balancing a DFG to achieve a desired target datathroughput, or due to buffer box storage granularity and latencyconstraints. In the example of FIG. 1 after the buffer inserter 104performs the latency analyses based on the intermediate DFG 130 and thebuffer allocator 118 inserts a number of buffers into the noncriticalpath, the buffer inserter 104 provides the output DFG 132 as an outputof the buffer insertion process implemented by the buffer inserter 104.Thereafter, the output DFG 132 can be used to configure PEs of the CGRAdevice 142 to structure the CGRA device 142 to implement the processdefined by the output DFG 132.

In some examples, the buffer allocator 118 determines that anotherbuffer resource is not available in the target CGRA device 142 to inserta further buffer in the input DFG 126. When this happens, and the inputDFG 126 is not yet latency-balanced, the buffer inserter 104 can insteadinsert a delay operation in the input DFG 126 to generate additionallatency in the noncritical path. To accomplish such additional latencygeneration in the noncritical path, the buffer inserter 104 is providedwith the example delay generator 120. For example, the delay generator120 inserts a delay operation in the noncritical path when the bufferallocator 118 determines that another buffer is not available forinsertion in the noncritical path to increase a similarity between thecritical path latency and the noncritical path latency.

Additionally or alternatively, if the buffer allocator 118 determinesthat sufficient buffer resources are not available in the target CGRAdevice 142 to insert a sufficient number of buffer(s) in the input DFG126 to latency-balance the DFG 126, a slackening process may be used torelax the buffer requirements for latency-balancing. Under such aslackening approach, the example buffer inserter 104 introduces a SLACKparameter into the buffer insertion analysis of the intermediate DFG 130to decrease a target data throughput of the DFG 126 to be less than one(e.g., less than one data token per logical clock cycle). In suchexamples, the SLACK parameter is a multiplier of the throughput equationaccording to Little's Law as described below in connection withConstraint 3. By varying the SLACK parameter to reduce the target datathroughput of a DFG, slackening can be used to reduce the number ofbuffers needed to sufficiently latency-balance the DFG such that the DFGsatisfies the target data throughput. Such a slackening approach isuseful when implementing examples disclosed herein in connection withCGRA devices having insufficient storage box resources to achieve ahigher target data throughput. Example slackening techniques may beimplemented in accordance with Constraint 3 described in greater detailbelow in which a SLACK constraint is multiplied by a throughputparameter of an edge (throughput_(i,j)) to decrease the target datathroughput of that edge. In some examples, slackening is implemented ona per-edge basis as each edge is analyzed for buffer insertion. In otherexamples, slackening is implemented on all edges of a DFG, and bufferinsertion is performed after such all-edge slackening. In some examplesin which buffer resources are depleted during a buffer insertion processof a DFG, any buffers inserted to that point are removed from the DFG sothat the slackening process can be performed again on all edges of theDFG. The buffer insertion process is then restarted based on theoriginal DFG (e.g., in the original state of the DFG before the previousbuffer insertion process inserted any buffer(s)). Such slackening andrestarting of the buffer insertion process may be repeated any number oftimes until the DFG is latency-balanced in accordance with a target datathroughput for which sufficient buffers are available.

FIGS. 2A-2C depict the example 126 of FIG. 1 including the examplenoncritical path 202 and the example critical path 204. For ease ofillustration, the example backedge 128 is not shown in FIG. 2A althoughthe input DFG 126 of FIG. 2A does include the backedge 128. As describedabove, examples disclosed herein insert buffers into noncritical pathsof DFGs to latency-balance noncritical paths and critical paths startingat the same starting nodes and terminating at the same ending nodes.Buffer insertion in a DFG (e.g., the DFG 126) means inserting buffers(i.e., storage) in the interconnecting network between two nodes in theDFG. For example, the input to the buffer insertion process describedabove in connection with FIG. 1 is the DFG 126 for which the bufferinsertion process produces the buffered output DFG 132 of FIG. 1 as anoutput. Buffer insertion in an interconnecting arc between nodes enablesholding more data which, in turn, increases latency tolerance. In a DFG,a node executes its operation as soon as all of the node's inputconnection arcs from preceding nodes have data ready and there is atleast one buffer at the node's output connection arc to hold the newoutput data to be generated by the node. According to Little's Law,throughput is equal to buffer divided by latency (e.g.,Throughput=Buffer/Latency). To improve throughput of a DFG, examplesdisclosed herein balance buffering in the DFG by performing overalllatency-balancing of the paths of the DFG. As such, examples disclosedherein are useful to implement a DFG performance optimization feature ofa compiler (e.g., the compiler 100 of FIG. 1) to improve throughputperformance of DFGs. For example, to improve throughput performance ofDFGs, examples disclosed herein adjust path latencies of noncriticalpaths to match or be substantially similar to the longest path latency(e.g., a critical path latency) of a DFG by inserting buffers in thenoncritical paths.

FIGS. 2A-2C show how the DFG 126 is imbalanced when the nodes o1-o6operate to process data. In the examples of FIGS. 2A-2C, ovalsenumerated 0, 1, 2 represent data tokens as inputs and/or outputs ofnodes, and connection arcs between the nodes represent flows of the datatokens guided by a producer-consumer relationship. For example, aproducer node generates an output data token that is consumed by aconsumer node. In examples disclosed herein, an operation of a node isdescribed as being performed during a logical clock cycle (e.g., onenode operation per logical clock cycle) such that a node consumes aninput data token, processes the input data token, and produces an outputdata token in a single logical clock cycle. As such, logical clockcycles can be used to refer to sequential stages of execution ofmultiple nodes of a DFG. Logical clock cycles differ from physical clockcycles in that a logical clock cycle is the demarcation betweenexecutions of nodes of a DFG in examples disclosed herein, and physicalclock cycles are tied to hardware operations (e.g., hardware operationsof PEs in CGRA devices that implement the nodes of a DFG) in which oneor more physical clock cycles implement a single logical clock cycle.For example, a PE of a CGRA device may perform multiple hardwareoperations over multiple physical clock cycles to execute a nodeoperation in a single logical clock cycle. However, examples disclosedherein may also be implemented in connection with DFGs in which multiplelogical clock cycles are used to execute a node operation for one ormore nodes of the DFG.

In the example of FIGS. 2A-2C, an external input data token to the DFG126 is provided to a starting node represented by the first node o1, anoutput data token of the DFG 126 is produced by an ending noderepresented by the fifth node o5, each of the nodes (o1, o2, o3, o4, o5,o6) can produce only one data token per logical clock cycle, and abuffer can only store one data token per connection arc between twonodes. In the example of FIGS. 2A-2C, the DFG 126 takes two logicalclock cycles for a data token to reach the ending node o5 from thestarting node o1 and the ending node o5 via the noncritical path 202,and the DFG 126 takes four logical clock cycles for a data token toreach the ending node o5 from the starting node o5 via the critical path204. For example, as shown in FIG. 2B, the noncritical path 202processes data token 0 in two logical clock cycles to reach the endingnode o5 (e.g., the first node o1 executes during a first logical clockcycle and the sixth node o6 executes during a second logical clockcycle). Concurrently, while the critical path 204 also processes thedata token 0 during the same two logical clock cycles, the data token 0does not yet propagate through the entirety of the critical path 204 toreach the ending node o5.

Each node o1-o6 of the example DFG 126 includes one input buffer perinput connection arc to hold an input data token form a preceding node.As such, since the DFG 126 of FIGS. 2A-2C can buffer or hold only onedata token per connection arc, by the time token 0 reaches the inputconnection arc between the sixth node o6 and the ending node o5 alongthe noncritical path 202, the noncritical path 202 begins exertingupward backpressure 206 because the ending node o5 needs input datatokens at both of its inputs to perform its operation. As such, beforethe data token 0 can be consumed by the ending node o5, advancement ofthe data token 0 is stalled in the noncritical path 202 until the datatoken 0 fully propagates through the critical path 204 to reach theending node o5. When the data token 0 stalls in the noncritical path 202before being consumed by the ending node o5, the data token 0 preventsthe data token 1 from advancing to the sixth node o6. As such, the datatoken 1 is stalled between the starting node o1 and the sixth node o6 inthe noncritical path 202. This stalling of the data tokens 0, 1 in thenoncritical path 202 creates the upward backpressure 206 on the startingnode o1. The upward backpressure 206 prevents the starting node o1 fromexecuting, which prevents data token 2 from entering the DFG 126. Thestalling and upward backpressure 206 causes a loss in data throughputperformance of the DFG 126.

Referring to the example of FIG. 2C, after four logical clock cycles,the ending node o5 will have data tokens 0 ready at both of its inputsat which time the ending node o5 can consume both inputs and execute itsoperation. This frees up the input buffer slots of the ending node o5for both the noncritical path 202 and the critical path 204. Freeing upthe input buffer slot of the ending node o5 for the noncritical path 202releases the upward backpressure 206. This allows the starting node o1to process data token 2 at the fourth logical clock cycle. In the fifthlogical clock cycle, data token 1 can retire (e.g., after beingprocessed by the ending node o5), and another external data token can beconsumed by the starting node o1 to enter the DFG 126. The processcontinues in this manner for additional external input data tokens.

FIG. 2C shows the example backedge 128 that represents a loop ortransfer of execution control from the ending node o5 to the second nodeo2 as the second node o2 waits without data at its input buffer in anidle state until the fourth logical clock cycle at which time thestarting node o1 provides the data token 2 to the second node o2. In theexample of FIGS. 2A-2C, the second node o2 operates on two inputs (e.g.,as noted based on the backedge 128 of FIG. 2C and the forward edgebetween the first node o1 and the second node o2). When the second nodeo2 executes for the first time, it receives a first input value from thestarting node o1 and receives a second input value seeded as an initialvalue at the output channel of the fifth node o5. Thereafter, furtherexecutions of the second node o2 are based on data from the startingnode o1 and data produced by the fifth node o5. Without modification,the DFG 126 of FIGS. 2A-2C processes two data tokens per four logicalclock cycles resulting in an effective data throughput or data-rate of0.5. This matches data throughput as defined by Little's Law (e.g., datathroughput of 0.5=2 data tokens/4 logical clock cycles). ApplyingLittle's Law to the data throughput of the DFG 126, two buffers can beinserted into the noncritical path 202 between the sixth node o6 and thefifth node o5 to obtain a throughput of one for the DFG 126.

FIGS. 3A-3C depict the example output DFG 132 of FIG. 1 including thetwo example buffers 136, 138 inserted in the noncritical path 202 ofFIGS. 2A-2C. With the two example buffers 136, 138 in the noncriticalpath 202, the data throughput of the DFG 132 is maximized because theinserted example buffers 136, 138 eliminate the need to stall thenoncritical path 202 at any logical clock cycle. For example, FIG. 3Ashows the starting node o1 passing data token 0 to the sixth node o6. Ina second logical clock cycle shown in FIG. 3B, the sixth node o6 is ableto store data token 0 in the first buffer 136 so that the sixth node o6can accept the data token 1 from the starting node o1. Similarly, at athird logical clock cycle, the first buffer 136 outputs data token 0 tothe second buffer 138 so that the first buffer 136 can consume datatoken 1 from the sixth node o6, and the sixth node o6 can consume datatoken 2 from the starting node o1. As shown in the example of FIG. 3C,at a fourth logical clock cycle, the ending node o5 consumes data token0 from the second buffer 138, the second buffer 138 consumes data token1 from the first buffer 136, the first buffer 136 consumes data token 2from the sixth node o6, and the sixth node o6 is able to consume datatoken 3 from the starting node o1. A similar producer-consumer processoccurs concurrently along the critical path 204 at the nodes o1-o5. Inthis manner, both the noncritical path 202 and the critical path 204process data at all logical clock cycles without the noncritical path202 stalling. In this manner, by inserting the buffers 136, 138 in thenoncritical path 202 (FIG. 2) of the input DFG 126 (FIGS. 1 and 2A-2C),the output DFG 132 (FIGS. 1 and 3A-3B) is latency-balanced to have anincreased data throughput relative to the input DFG 126. That is, thelatency-balanced output DFG 132 has an increased data throughput becauseeach node o1-o6 executes its operation once per logical clock cycle, andthe noncritical path 202 of the input DFG 126 need not stall consumptionof a subsequent data token at the starting node o1 after the secondlogical clock cycle. As also shown in FIGS. 3A-3C and in FIG. 1, whenthe input to the buffer insertion process is a cyclic DFG (e.g., theinput DFG 126 of FIG. 1), the output of the buffer insertion process isalso a cyclic DFG which includes the previously removed backedges (e.g.,the backedge 128) in addition to the inserted buffers (e.g., theinserted buffers 136, 138). Backedges of an input DFG should comeproperly buffered (either when generated by a compiler or when writtenby a programmer) to ensure correctness of the DFG.

The above examples of FIGS. 2A-2C and FIGS. 3A-3C show that insertingbuffers into some connection arcs of a DFG may be used to improve datathroughout in a DFG. Examples disclosed herein facilitate determininghow much buffering to insert and where to insert the buffers using aprocessor-implemented algorithmic techniques. Examples disclosed hereinprovide latency-balancing solutions by using a constraint-based linearprogramming optimization problem for which the quantity of buffersinserted in a DFG is minimized while maximizing data throughputperformance of the DFG. When the number of buffers is fixed (e.g., dueto limited buffer resources in a target device), the optimizationproblem is to optimize the overall throughput or minimize the loss inthroughput given the buffer budget.

A CGRA device can be synchronous or asynchronous. A synchronous CGRAdevice has a global clock and data moves at each logical clock cycle.Although prior techniques provide buffer insertion solutions forsynchronous dataflow architectures, examples disclosed herein are usefulfor inserting buffers in DFGs that run on asynchronous CGRA devices. Anasynchronous CGRA device often has no global clock, and theinterconnecting arcs and PEs can have variable data rates which makes itmore difficult to solve the buffer insertion problem. Examples disclosedherein may be employed to insert buffers in DFGs written forasynchronous CGRA devices by employing an algorithmic computationalprocedure to optimally insert buffers on edges (e.g., noncritical paths)in a general DFG. In addition, examples disclosed herein can beimplemented in connection with asynchronous CGRA architectures and/orsynchronous CGRA architectures.

Prior techniques for inserting buffers are directed to buffer insertionon directed acyclic graphs (DAGs) implemented for synchronous systems.However, most computer programs contain cycles. For example, a computerprogram contains cycles when it includes a “while loop” or nested loopswith inner loop dependencies. Such types of loops are often present incomputer programs. To perform a buffer insertion process, examplesdisclosed herein first perform a backedge detection and annotationprocess to detect backedges in input DFGs (e.g., the input DFG 126) andannotate the backedges in the DFGs. In this manner, the subsequentbuffer insertion process can remove the annotated backedges from theDFGs to latency-balance the DFGs by inserting a suitable number ofbuffers in one or more noncritical paths.

Examples disclosed herein perform backedge detection by analyzing DFGsfor dominant nodes and return paths to those dominant nodes. A node ‘x’in a flow graph dominates node ‘y’ if every path from the source node to‘y’ goes through node ‘x’. As such, every node dominates itself and thesource node dominates every other node in the DFG. For example, the testcondition of a while loop dominates all blocks in the body of the whileloop. Similarly, the test of an if-then-else statement dominates allblocks in either branch. During analysis time, the example backedgedetector 102 of the compiler 100 (FIG. 1) can detect backedges byrunning a suitable graph-traversal analysis (e.g., a depth-first search(DFS) traversal, a breadth-first-search (BFS) traversal, a post-ordertraversal (left-right-root), etc.) and then detecting retreating edgesand backedges. A retreating edge is an edge that goes from a node to itsancestor in a traversal order. This includes a self-loop that goes froma node to itself. An example manner of detecting retreating edges is toperform a post-order traversal and detect all edges that go from ahigh-ranked node to a low-ranked node in the reverse ordering of thatpost-order traversal. The characteristic detector 106 (FIG. 1) can tagthose detected high-to-low node-transition edges as retreating edges.The characteristic comparator 108 can confirm a retreating edge as abackedge if its head node (e.g., a loop start node) dominates its tailnode (e.g., a loop end node). Although every backedge is a retreatingedge in a traversal order analysis of a DFG, not every retreating edgeis a backedge. Examples disclosed herein use such graph-traversalanalyses to detect backedges, annotate the backedges in DFGs, and removethe annotated backedges to generate acyclic DFGs (e.g., the intermediateDFG 130 of FIG. 1). In this manner, examples disclosed herein cananalyze the acyclic DFGs to determine optimal quantities of buffers toinsert into the DFGs to latency-balance their paths and, in turn,improve data throughput capabilities of the DFGs. A challengeencountered in latency-balancing DFGs is that the problem of deleting aminimal set of backedge connection arcs to create a directed acyclicgraph from an arbitrary graph is known to be NP-complete. The acronym NPstands for nondeterministic polynomial time. A problem that isNP-complete means that although a solution to the NP-complete problemcan be verified quickly, there is no known way to find a solutionquickly. That is, the time required to solve the problem using anycurrently known algorithm increases rapidly as the size of the problemgrows. As such, processing large DFGs can require a significant amountof time. However, examples disclosed herein leverage topologycharacteristics of DFGs to perform backedge detection and annotation.For example, the dataflow graphs have designated start and end nodes,and backedges have specific properties based on topologies of theirDFGs, which examples disclosed herein leverage to perform backedgedetection and annotation in an efficient manner.

FIG. 4 illustrates example source code 402 in the C programming languagefor a cyclic computer program containing a while loop, correspondingassembly code 404, and a corresponding cyclic DFG 406 of the operationsset forth in the assembly code. The example assembly code 404 is acompiler IR representation. For example, the compiler IR representationmay be a machine-specific LLVM IR representation or a general LLVM IRrepresentation. In the example assembly code 404 of FIG. 4, the .licmnemonic represents a connection arc in the DFG 406, the word next tothe .lic mnemonic denotes its type and the next word denotes the name ofthe .lic mnemonic. A pick operation in the DFG 406 picks between twoinputs (e.g., in_ctl and i_loopback in the assembly code 404) based onthe value of cmp_0 (in the assembly code 404) which starts with aninitial value of 0 and gets a new value based on a loop terminationcondition comparison (e.g., i<10 or cmplts64 cmp, i_next_1, 10 in theassembly code 404). The add operation in the DFG 406 computes thepotential next value of i, and the copy operation in the DFG 406 takes avalue and produces multiple copies of its input to feed otheroperations. The cmp operation of the DFG 406 compares the i_next withthe loop boundary 10 (e.g., cmplts64 cmp, I next 1, 10 in the assemblycode 404). The result of the cmp operation is copied to two differentdestinations as values cmp_0 and cmp_1. The cmp_0 value is used toswitch the i_next value to i_loopback or to i_result based on the cmpltsoutput which triggers the output signal. As shown in FIG. 4, the whileloop of the source code 402 and corresponding loopback instructions ofthe assembly code 404 result in the DFG 406 containing cycles. Examplesdisclosed herein provide a buffer insertion solution to insert buffersin cyclic DFGs that contain cycles/loops such as the example DFG 406.Examples disclosed herein improve on prior buffer insertion solutions.For example, prior buffer insertion solutions do not address the problemthat when a buffer is inserted in a forward edge of a cycle, such bufferinsertion can increase the latency of a corresponding cycle/loop, thus,reducing the overall data throughput of the DFG. Using examplesdisclosed, buffers can be inserted without reducing data throughput.Instead, example buffer insertion techniques disclosed herein increasedata throughput of a DFG.

Still referring to FIG. 4, buffer insertion examples disclosed hereininvolve annotating backedges in DFGs, as described above in connectionwith FIG. 1. To perform backedge annotation in accordance with examplesdisclosed herein, the source code 402 (in a high-level programminglanguage such as the C programming language) can be provided to thecompiler 100 of FIG. 1 to generate the corresponding assembly code 404and DFG 406. The backedge detector 102 of FIG. 1 can then analyze theDFG 406 to annotate backedges. As such, examples disclosed herein enableproviding the example compiler 100, which is capable of generatingassembly code from a program written in a high-level programminglanguage such as C/C++/Fortran, with capabilities to annotate backedgesof cyclic DFGs. In the example of FIG. 4, such backedge annotation canbe performed by the backedge detector 102 (FIG. 1) of the compiler 100inserting a backedge attribute such as “.attrib backedge” 408 precedingan edge declaration in the dataflow assembly code 404.

Examples disclosed herein leverage topology awareness capabilities ofthe compiler 100 to perform backedge detection and annotation. Forexample, the compiler 100 has complete topology information of an inputprogram as well as the corresponding dataflow IR because the compiler100 generates the LLVM IR from the high-level language description ofthe source code 402. The compiler 100 generates information describingwhich code belongs to a loop and what interconnect arc represents thebackedge in the loop that feeds back a new value for each loopinvariant. By leveraging the graph topology information of the compiler100, as well as loop membership information, examples disclosed hereinuse such information to enhance capabilities of the compiler 100 toannotate backedges in the generated dataflow code. This provideseffective and efficient backedge annotation and buffer insertionsolutions in the compiler 100.

By detecting and annotating backedges in cyclic DFGs, examples disclosedherein enable buffer insertion to work on input DFGs that are cyclic andasynchronous. That is, by detecting and annotating backedges in DFGs inaccordance with examples disclosed herein, the example compiler 100(FIG. 1) can convert an input DFG that contains cycles or loops (e.g.,the input DFG 126 of FIGS. 1, 2A-2C, and 3A-3C) into an acyclic DFG(e.g., the intermediate DFG 130 of FIG. 1) by removing annotatedbackedges between child and parent operations. In particular, after theexample backedge detector 102 (FIG. 1) annotates backedges in an inputcyclic DFG, the example buffer inserter 104 (FIG. 1) converts the inputcyclic DFG into an acyclic DFG, and solves the buffer insertion problemfor the acyclic DFG using a constraints-based linear programming solver(or any other suitable solver or algorithmic format) while substantiallyreducing or eliminating a likelihood of adding additional latency inperformance-critical loops. Absent examples disclosed herein, priorbuffer insertion techniques are unable to optimize many dataflowprograms that contain loops and cycles. For example, techniquesdisclosed herein can be used to latency-balance a DFG of a binary-searchprogram and/or any other program which contains multiple cycles toincrease data throughput of such programs.

FIG. 5 represents an example high-level workflow 500 of the compiler 100of FIG. 1 to compile and optimize DFGs. The example high-level workflow500 includes backedge detection and annotation examples disclosed hereinand buffer insertion examples disclosed herein to increase datathroughput of DFGs. The example workflow 500 is implemented by thecompiler 100 to latency-balance DFGs by inserting buffers in accordancewith algorithm-based processor-implemented analyses disclosed herein toincrease data throughput of DFGs. The example workflow 500 includesmultiple stages shown as stage_0 504 through stage_5 514. In otherexamples, the complier 100 may be implemented with fewer or more stages.Also, in other implementations, features shown in FIG. 5 as performed ina particular stage may alternatively be performed in other stages of theworkflow 500.

At an example stage_0 504 of FIG. 5, the example compiler 100 receivesan input DFG (e.g., the input DFG 126 of FIGS. 1, 2A-2C, and 3A-3C) as aportable assembly representation which is a high-level description of acomputer program or compute kernel. The input DFG may be written in ortranslated from a high-level programming language or a low-levelprogramming language. At an example stage_1 506, the example compiler100 processes the input DFG to create an internal graphicalrepresentation with visually perceivable nodes (e.g., viewable via agraphical user interface) representing operations of the DFG andconnection arcs representing paths or edges of data flow between thenodes. Example graphical representations are shown in FIGS. 2A-2C,3A-3C, and FIG. 5. At an example stage_2 508, the example compiler 100binds the DFG to specific target hardware (e.g., the CGRA device 142 ofFIG. 1) to account for resource characteristics (e.g., quantities andtypes of PEs, quantities/sizes of storage boxes, latency/buffercharacteristics, and/or other metadata pertaining to target devicecharacteristics) of the target hardware. At the example stage_2 508, thecompiler 100 labels edges between nodes with hardware-specificcharacteristics of the target device such as latency and pre-existingbuffering (e.g., buffers existing in the original input DFG). At anexample stage_3 510, the compiler 100 implements example backedgedetection and annotation techniques disclosed herein as well as examplebuffer insertion techniques disclosed herein. At an example stage_4 512,the compiler 100 produces an optimized, machine-bound DFG (e.g., theoutput DFG 132 of FIGS. 1, 2A-2C, and 3A-3C) as an output which can beused by subsequent tools of a CGRA development platform. At an examplestage_5 514, the compiler 100 generates or writes the output DFG to anoutput file (e.g., in a high-level programming language or a low-levelprogramming language). In some examples, the output file can beinspected by a programmer.

Examples disclosed herein may be implemented in stage_3 510 of theworkflow 500. For example, at stage_3 510, the backedge detector 102analyzes the input DFG 126 by traversing the DFG 126 to find cycles andidentify backedges in those cycles. Example techniques for analyzing theinput DFG 126 for detecting and annotating backedges are described belowin connection with FIGS. 6-9. Also at stage_3 510, the example bufferinserter 104 breaks cycles in the input DFG 126 by removing thebackedges annotated therein by the backedge detector 102 to generate theintermediate DFG 130 of FIG. 1. In addition, the example buffer inserter104 marks sink nodes of removed backedges as loop start nodes and sourcenodes of removed backedges as loop end nodes. For example, in theintermediate DFG 130 shown in FIG. 1, the buffer inserter 104 labelsnode o5 as a loop end node by storing a loop end identifier in thememory 124 in association with the instruction(s) corresponding to thenode o5. Similarly, the example buffer inserter 104 labels node o2 as aloop start node by storing a loop start identifier in the memory inassociation with the instruction(s) corresponding to node o2. Theexample buffer inserter 104 can run backedge detection analyses usingany suitable technique from all unvisited nodes of a DFG to detectbackedges for subsequent removal and breaking of simple cycles in theDFG.

Examples disclosed herein may be implemented in connection with otherprocesses that confirm all backedges of a DFG are buffered properly byusers or a compiler or a smart code generator. In this manner, cycles inthe DFG do not cause deadlock during execution. For purposes of examplesdisclosed herein, it is assumed that such proper buffering of backedgesis confirmed through suitable techniques.

FIG. 6 is an example DFG 600 showing backedges annotated by the examplebackedge detector 102 of FIG. 1 using a Depth-First Search (DFS)technique. The DFG 600 includes nodes (e.g., vertices) interconnected byconnection arcs. FIG. 7 depicts example DFS pseudocode 700 representingcomputer-readable instructions that may be executed by a processor(e.g., the processor 1412 of FIG. 14) to structure the backedge detector102 to perform DFS analyses to detect and annotate backedges in DFGs.The example backedge detector 102 performs multiple passes of a DFGduring a DFS analysis, and each DFS pass is performed per logical clockcycle of the DFG. For each logical clock cycle, the characteristicdetector 106 (FIG. 1) of the backedge detector 102 detects an executionstatus of each vertex/node of the DFG 600 and tags or labels eachvertex/node with a node characteristic identifier indicative of anexecution status of that vertex/node. In this manner, the backedgedetector 102 can perform comparisons based on node characteristicidentifiers and reference criteria to detect where backedges occur atones of the nodes. For example, the backedge detector 102 can run a DFSanalyses in accordance with the DFS pseudocode 700 and color unvisitedvertices as white nodes, currently being executed vertices as graynodes, and finished vertices as black nodes. In the illustrated example,the colors white, gray, and black are used to represent different nodecharacteristic identifiers which include an unexecuted-statusidentifier, an executing-status identifier, and a completed-statusidentifier. For example, the color white represents theunexecuted-status identifier to indicate that an unvisited vertex hasnot yet been executed, the color gray represents the executing-statusidentifier to indicate that a currently visited node is in the processof being executed, and the color black represents the completed-statusidentifier to indicate that no further executions of a node are to occurduring execution of the DFG. In other examples, other colors oridentifying information may be used instead of white, gray, and/orblack.

After marking nodes of the DFG 600 with corresponding first nodecharacteristic identifiers during a first logical clock cycle, thebackedge detector 102 performs a similar analysis on the nodes toidentify their execution statuses as second node characteristicidentifiers during a second logical clock cycle. Also at the secondlogical clock cycle, the example characteristic comparator 108 (FIG. 1)of the backedge detector 102 compares the first node characteristicidentifiers identified during the first logical clock cycle with thesecond node characteristic identifiers of the second logical clock cycleto detect backedges. In the illustrated example, ones of the second nodecharacteristic identifiers set to executing-status identifiers aredesignated as a reference criterion such that when the characteristicdetector 106 detects a node is being executed during the second logicalclock cycle and designates that node with an executing-statusidentifier, the characteristic comparator 108 compares the nodecharacteristic identifier of the previous, first logical clock cycle forthat node with the reference criterion (e.g., the executing-statusidentifier) of that node for the current, second logical clock cycle. Insuch examples, the characteristic comparator 108 confirms a match whenthe node characteristic identifier of the previous logical clock cyclefor that node is the executing-status identifier, thus matching thereference criterion. That is, when a node is labeled as executing duringa previous logical clock cycle, and that node is revisited for executionduring a subsequent logical clock cycle, this means that executioncontrol was transferred back to that node via a backedge. A backedgeconfirmed by the characteristic comparator 108 is represented by a cycleand an edge that goes from a child node to a parent/ancestor node. Thebackedge identifier generator 110 generates backedge identifiers forbackedges confirmed by the characteristic comparator 108, and annotatesthe backedges in the memory 124 (FIG. 1). For example, the backedgeidentifier generator 110 stores backedge identifiers (e.g., bit values,string values, mnemonics, etc.) in records or entries or as lines ofcode corresponding to ones of the connection arcs identified asbackedges. An example of a mnemonic-based backedge annotation is theassembly code attribute “.attrib backedge” 408 described above inconnection with FIG. 4. In the illustrated example of FIG. 7, theannotation instruction is represented by G_DAG.annotate(e(u,v)). Inother examples, in addition to or instead of annotating backedges, thecomputer-readable instructions represented by the DFS pseudocode 700 ofFIG. 7 may directly remove backedges. In such other examples, to removebackedges, the annotation instruction G_DAG.annotate(e(u,v)) may besupplemented with or replaced by a backedge removal instructionG_DAG.remove(e(u,v)).

When the backedge detector 102 is configured to use DFS to detectbackedges, the DFS analysis should start from a true source node. If theDFS is not run from a true source node, the DFS analysis may choose abackedge that is not the best backedge to remove from a dataflowprogram's perspective. For example, referring to the DFG 600 of FIG. 6,which corresponds to a binary-search algorithm, if the backedge detector102 performs a DFS traversal starting from the “min” node, thecrossed-out edges will be identified as backedges and, thus, will beremoved by the buffer inserter 104 to make the graph acyclic. The DFSanalysis would identify different backedges if the DFS traversal startedfrom the “max” node. To select true source nodes, the backedge detector102 uses metadata of programs' DFGs to identify true source nodes whichare directly connected to external inputs and not dependent on internalinputs from internal nodes.

In some examples, the DFS technique may be combined with Johnson'salgorithm, which is a method of finding the shortest paths between pairsof vertices (e.g., nodes) in a sparse, edge-weighted, directed graph(e.g., a DFG). Johnson's algorithm is named after Donald B. Johnson, whopublished the technique in a journal article titled, “Finding All TheElementary Circuits of a Directed Graph,” SIAM J. Comput., Vol. 4, No.1, March 1975. Using DFS and Johnson's algorithm, the backedge detector102 (FIG. 1) detects the simple cycles in a DFG and annotates the edgesstarting at child nodes and ending in parent nodes in DFS order asbackedges. Without any topology information of a DFG, a challenge inusing the DFS technique is that detecting the minimum number ofbackedges of the DFG to remove to make the DFG acyclic has been shown tobe NP-complete, as discussed above. However, examples disclosed hereinovercome such minimal set backedge removal problem by using topologyinformation obtained by the compiler 100 about the source-sink noderelationships in input DFGs. In this manner, the backedge detector 102can annotate backedges between child and parent nodes by implementingthe DFS technique based on topologically sorted source nodes inside acycle.

FIG. 8 depicts example pseudocode 800 of computer-readable instructionsthat may be executed by a processor (e.g., the processor 1412 of FIG.14) to structure the backedge detector 102 to perform Breadth-FirstSearch (BFS) analyses to detect and annotate backedges in DFGs. Toimplement a BFS analysis, the backedge detector 102 starts from a truestart node (e.g., a node at which an external input is received and isnot dependent on internal inputs from internal nodes). The examplecharacteristic detector 106 (FIG. 1) labels all the nodes of the DFGwith characteristic identifiers representing execution depths orhierarchy levels which represent enumerated sequential orders in whichthe nodes execute. For example, the sequential ordering of execution ofthe nodes corresponds to a sequential ordering of logical clock cyclesat which the nodes undergo their first instances of execution. Forexample, the characteristic detector 106 labels the true start node witha depth of 0 and all other nodes of the DFG with a node characteristicidentifier of infinite. In this example, the node characteristicidentifier of infinite is a default reset node characteristic identifierrepresenting that those nodes have not yet been executed. The examplecharacteristic detector 106 traverses the DFG in a level-by-level mannerand assigns a depth value (e.g., a node characteristic identifier) toeach node based on their earliest discovery time (e.g., the logicalclock cycle of their first execution).

After the characteristic detector 106 labels each node with its shortestdistance (e.g., depth value) from the source node, the examplecharacteristic comparator 108 (FIG. 1) iterates through all edges of theDFG. The example characteristic comparator 108 determines: (1) if thesource node at which an edge starts is a higher depth level node (e.g.,a node characteristic identifier) and the sink node at which the edgeends is a lower depth level node (e.g., a node characteristicidentifier), and (2) if the sink node of the edge is an ancestor of thesource node of the edge. If both are true, the characteristic comparator108 confirms it has detected a cycle, and the backedge identifiergenerator 110 (FIG. 1) annotates the corresponding edge as a backedge asdescribed above. In the comparisons performed by the characteristiccomparator 108, one of the node characteristic identifiers represents areference criterion. For example, for an edge between an ancestor nodeand a child node, if the node characteristic identifier of a higherdepth level source node (child node) is the reference criterion, thenthe characteristic comparator 108 confirms a backedge flowing from thechild node to the ancestor node when a comparison confirms that the nodecharacteristic identifier of the lower depth level sink node (ancestornode) is a lower depth value than the depth value of the referencecriterion corresponding to the higher depth level sink node (childnode). Alternatively, if the node characteristic identifier of a lowerdepth level source node (ancestor node) is the reference criterion, thenthe characteristic comparator 108 confirms a backedge flowing from thechild node to the ancestor node when a comparison confirms that the nodecharacteristic identifier of the higher depth level source node (childnode) is a higher depth value than the depth value of the referencecriterion corresponding to the lower depth level sink node (ancestornode). In the illustrated example of FIG. 8, the annotation instructionis represented by G_DAG.annotate(G). In other examples, in addition toor instead of annotating backedges, the computer-readable instructionsrepresented by the pseudocode 800 of FIG. 8 may directly removebackedges. In such other examples, to remove backedges, the annotationinstruction G_DAG.annotate(G) may be supplemented with or replaced by abackedge removal instruction G_DAG.remove(G).

FIG. 9 depicts example pseudocode 900 representing computer-readableinstructions that may be executed by a processor (e.g., the processor1412 of FIG. 14) to structure the backedge detector 102 to performpost-order traversal and dominator analyses to detect and annotatebackedges in DFGs. In post-order traversal and dominator analysis, thebackedge detector 102 (FIG. 1) first traverses a DFG in post-order andfinds a dominator set of nodes for each node/vertex. A node ‘x’ in a DFGdominates a node ‘y’ if every path from the source node to the node ‘y’goes through the node ‘x’. The example backedge detector 102 then usesnode characteristic identifiers of dominator and dominated nodes todetermine when edges between the nodes are backedges. The backedgeidentifier generator 110 (FIG. 1) annotates the corresponding edge as abackedge as described above.

In other examples, techniques disclosed herein may be implemented inconnection with manual backedge annotation. In such examples,programmers manually annotate backedges when they program DFGs inassembly language by inserting backedge identifiers (e.g., backedgeattribute mnemonics) in the assembly code of the DFGs. The manuallyannotated backedges can then be removed by the buffer inserter 104(FIG. 1) to convert cyclic DFGs into acyclic DFGs. Although manualbackedge annotation can be performed, it is more error prone thanautomatic compiler-implemented techniques and can also betime-consuming. When manual backedge annotation is used, the compiler100 (FIG. 1) can be used to run backedge detection and annotation toensure that all backedges are properly annotated so that backedgeremoval successfully generates an acyclic DFG.

After annotating backedges, the example buffer inserter 104 of FIG. 1removes the annotated backedges and inserts buffers. That is, after thebuffer inserter 104 makes a DFG acyclic by removing backedges from theDFG and marking all loop start nodes and loop end nodes (e.g., as shownin the intermediate DFG 130 of FIG. 1), the buffer inserter 104 solvesthe buffer insertion problem in the DFG by solving a set ofconstraint-based linear programming equations representing buffering andlatency constraints on each connection arc in the DFG. In otherexamples, the buffer insertion problem in the DFG may be solved usingany other suitable solver or algorithmic format instead of or inaddition to constraint-based linear programming.

Example processor-implemented algorithmic techniques that can beimplemented by the buffer inserter 104 to insert buffers in DFGs can bebased on the following disclosed examples. Table 2 below definesvariables of the following example equations.

TABLE 2 Definitions of Buffer Insertion Variables Variable Descriptionu_(i) Firing time/start time of an operation i W_(i,j) Latency of anedge e(i, j) box_(i,j) The number of storage boxes on edge e(i, j) CCapacity in each storage box, constant k Latency of each storage box,constant SLACK A loss term for throughput or a throughput modulationterm 0 < SLACK <= 1 throughput_(i,j) Throughput of edge e(i, j)hops_(source,sink) Maximum number of arcs/edges that are present in anypath from a source to a sink

In Table 2 above and in examples disclosed herein, the terms buffer andstorage box are used interchangeably. In addition, the terms edge, arc,connection arc, and interconnecting arc are used interchangeably. Inexamples disclosed herein, the dataflow architectures (e.g., CGRA,Intel's CSA, etc.) of target devices (e.g., the CGRA device 142 ofFIG. 1) have elastic buffering instead of synchronous buffering. Forexample, elastic buffering arises when an inserted buffer capacity canbe varied relative to latency, while synchronous buffering is directlyproportional or fixed to storage box capacity. Examples disclosed hereinmay be implemented in connection with elastic buffering and/orsynchronous buffering. As such, changes in latency are not directlyrelated to changes in capacity/buffering. Also in examples disclosedherein, each buffer resource has a constant k latency, and has acapacity C such that k≤capacity≤C. Also in examples disclosed herein,buffers are inserted only in a discrete size of C, and the buffer sizeis selectable to be any suitable capacity within the constraintcapacity≤C of a storage box. For any acyclic DFG (e.g., abackedge-removed DFG such as the intermediate DFG 130 of FIG. 1), thefollowing equations may be used to implement examples disclosed hereinto insert buffers in the DFG.

Latency Equation

If operation j has a dependency on operation i, then the latencyconstraint for the inter-dependent operations i and j is defined by thelatency-constraint equation u_(j)≥W_(i,j)+u_(i). If a quantity ofbox_(i,j) buffers needs to be added on a connection arc e(i,j) tolatency-balance a DFG, and if each buffer has a latency k, the abovelatency-constraint equation is updated to be(u_(j)−u_(i))≥W_(i,j)+k*box_(i,j). The per-edge latency constraint isdefined as shown in Constraint 1 below for each connection arc/edge.∀edge(i,j)(u _(j) −u _(i))≥W _(i,j) +k*box _(i,j)  Constraint 1

Constraint 1 above can be implemented in the example buffer inserter 104of FIG. 1 to determine quantities of buffers to insert in noncriticalpaths. For example, the buffer inserter 104 can use the latencycalculator 114 and the latency comparator 116 of FIG. 1 to determine thenumber of buffers to insert into noncritical paths without exceeding acritical path latency of a DFG. In Constraint 1 above, for each edge (∀edge(i,j)), the difference between start times of operations i and j((u_(j)−u_(i))) is greater than or equal to the sum of: (a) the latencyof that edge (W_(i,j)) and (b) the product of the latency of each bufferand the quantity of buffers on that edge (k*box_(i,j)). In examplesdisclosed herein, the buffer latency (k) of a buffer is one or morelogical clock cycles. One or more logical clock cycles is also equal tothe latency of a PE of a CGRA device to execute an operation of a node.However, in other examples, a buffer may have a latency less than alogical clock cycle. In some examples (e.g., as is the case in elasticbuffering), one or more buffers may be aggregated in a manner that doesnot increase the latency of the aggregation beyond the latency of a unitsingle buffer. Such an aggregation may have a latency of one or morelogical clock cycles.

Capacity Equation

If the interconnecting arc e(i,j) of operation i and j has a throughputof throughput_(i,j), then according to Little's Law which statesthroughput=Buffer/Latency, a buffer constraint can be written as shownin Constraint 2 below.∀edge(i,j)box _(i,j) *C≥throughput_(i,j)*(u _(j) −u_(i))−capacity_(i,j)  Constraint 2

If a target CGRA device does not have enough storage boxes to balancelatency in a DFG, the throughput can be slackened by a given SLACK rate.As noted above, the best achievable throughput of a DFG is 1. Byslackening, a desired data throughput is adjusted to be less than 1(e.g., less than one data token per logical clock cycle). As such, theoverall capacity of the storage boxes added on a connection arc e(i,j)is configured to tolerate the throughput-modulated latency (e.g., theslackened latency) minus any pre-existing capacity_(i,j) on theconnection arc e(i,j). In examples disclosed herein, all edges of a DFGcan be slackened uniformly, or slackening can be performed on a per-edgebasis such that throughput can be modulated differently across differentedges of the DFG. To determine the amount of SLACK to add to a path, thedelay generator 120 uses the SLACK constraint as defined in Constraint 3below.∀edge(i,j)box _(i,j) *C≥SLACK*throughput_(i,j)*(u _(j) −u_(i))−capacity_(i,j)  Constraint 3

Constraint 3 above can be implemented in the example delay generator 120to determine an amount of delay or SLACK to configure in noncriticalpaths. In Constraint 3 above, for each edge (∀ edge(i,j)), a product ofthe quantity of buffers on an edge and the capacity of each buffer(box_(i,j)*C) is greater than or equal to the difference between: (a)the product of a generated delay (SLACK multiplier), the throughput ofthe edge, and the start time difference between interdependentoperations i and j (SLACK*throughput_(i,j)*(u_(j)−u_(i))) and (b) thetotal capacity of the edge (capacity_(i,j)). For example, the totalcapacity is the capacity sum of any pre-existing storage (e.g.,buffer(s)) in the edge and any additional buffer(s) inserted in theedge.

Additionally or alternatively, the example delay generator 120 (FIG. 1)can insert a delay operation in a noncritical path when sufficientbuffers are not available for insertion in the noncritical path toincrease a similarity between a critical path latency and a noncriticalpath latency to sufficiently latency-balance the DFG. In such examples,the delay operation can provide the additional latency and capacity thatwould be provided by an inserted buffer.

Critical Path Latency Constraint

In some examples in which it is desired to increase a latency of thecritical path to facilitate latency-balancing a DFG, the example bufferinserter 104 (FIG. 1) finds a solution for u_(i) such that the longestpath latency difference between the source node and the sink node of anedge does not increase the critical path latency of the DFG prior tobuffer insertion. If each connection arc on the critical path gets onebuffer in the worst case, the maximum increase in latency is defined ashops_(source,sink)*k. To have a rough upper bound on how much thecritical path latency can be increased, the buffer inserter 104 addshops_(source,sink)*k to the critical path latency. As such, the criticalpath latency constraint is represented as shown in Constraint 4 below.u _(sink) −u _(source) ≤W _(source,sink)+hops_(source,sink)*k  Constraint 4

In Constraint 4 above, the difference between start times of the sinkand source nodes (u_(sink)−u_(source)) is less than or equal to the sumof: (a) the latency of that edge (W_(source,sink)) and (b) the productof the maximum number of hops between the sink and source nodes(hops_(source,sink)) and the buffer latency (k).

Critical Path Latency Constraint for any I/O Pair

In some examples, a critical path latency constraint per I/O data paircan be performed to facilitate latency-balancing a DFG. A DFG can havemultiple inputs and outputs. For each input-output pair in the DFG, theexample buffer inserter 104 (FIG. 1) protects against a buffer insertionsolution that increases the critical path latency of the DFG in asimilar way as described above for the source-sink critical path latencycase. As such, to eliminate or substantially decrease the likelihood ofincreasing a critical path latency in a DFG, the example latencycalculator 114 and example latency comparator 116 of FIG. 1 implementthe critical path latency constraint of Constraint 5 below.∀(I,O)u _(O) −u _(I) ≤W _(I,O)+hops_(I,O) *k  Constraint 5

In Constraint 5 above, for each pair of input data and output data (∀(I,O)), the difference between the start times of consuming input data andproducing corresponding output data (u_(O)−u_(I)) at corresponding nodesis less than or equal to the sum of: (a) the latency of thecorresponding edge (W_(I,O)) and (b) the product of the maximum numberof hops between the input-output data pair (hops_(I,O)) and the bufferlatency (k).

Storage Box Budget Equations

The example buffer allocator 118 (FIG. 1) monitors buffer allocation sothat the number of storage boxes on each connection arc is non-negative,and the sum of all storage boxes is within the maximum storage boxesavailable on the target CGRA device (e.g., the CGRA device 142 of FIG.1). The buffer allocator 118 uses this storage box quantity constraintas represented in Constraint 6 below.∀e(i,j)box _(i,j)≥0,∀e(i,j)Σbox _(i,j)≤Max Storage Boxes  Constraint 6

In Constraint 6 above, for each edge (∀ e(i,j)), the number of storageboxes is greater than or equal to zero, and for each edge (∀ e(i,j)),the total quantity of storage boxes on that edge (Σbox_(i,j)) is lessthan or equal to the maximum quantity of storage boxes (Max StorageBoxes) available on the CGRA device.

Optimization Goal

In some examples, the buffer inserter 104 inserts a quantity of buffersthat contribute towards an optimization goal to maximize data throughputof a DFG. An example of such an optimization goal is represented inEquation 1 below.Optimized DFG Throughput=MaximizeΣSLACK*throughput_(i,j)  Equation 1

In some examples, the buffer inserter 104 can employ other optimizationgoals in addition to or instead of the above throughput optimization.Examples of other optimization goals include Maximize (minimum(SLACK_(i,j))), where SLACK_(i,j) denotes independent SLACK applied toeach edge. If a target CGRA device has unlimited storage, an exampleoptimization goal is to minimize the quantity of storage boxes(minimizeΣbox_(i,j)) to not exceed the critical path latency.

The example buffer inserter 104 (FIG. 1) can also implement an iterativeslackening approach to buffering a DFG. For example, the delay generator120 (FIG. 1) starts with a SLACK value 1 and multiplies throughputs ofall edges by the SLACK value so that the buffer inserter 104 candetermine a buffering solution that minimizes the total buffers insertedin the DFG. If the obtained solution requires more buffers thanavailable, the delay generator 120 decreases the SLACK value (e.g.,SLACK=0.9) and repeats the process, until the buffer inserter 104 findsa solution that fits the budget (e.g., maximum available storage boxes)with a maximum possible SLACK value.

Avoiding Latency in Critical Loops

In some examples, adding additional latency to a loop decreases itsoverall data throughput. To eliminate or substantially decrease thelikelihood of adding additional latency to the original cycles, thebuffer inserter 104 can be configured to add an additional constraintcalled Loop Latency Constraint, as represented in Constraint 7 below.∀(loopStart,loopEnd)u _(loopEnd) −u _(loopStart) ≤W _(loopStart,loopEnd)+hop _(loopStart,loopEnd) *k*LOOP_(loopStart,loopEnd)  Constraint 7

In Constraint 7 above, for each loop start node and corresponding loopend node, the difference between start times of the loop start and loopend nodes (u_(loopEnd)−u_(loopStart)) is less than or equal to the sumof: (a) the latency of that edge (W_(loopStart,loopEnd)) and (b) theproduct of the maximum number of hops between the loop start and loopend nodes (hops_(loopStart,loopEnd)) and the buffer latency (k). InConstraint 7, LOOP_(loopStart,loopEnd) is a modulation term which is setbased on the criticality of the loop. If a loop is not on the criticalpath of the main DFG, the buffer inserter 104 sets a value ofLOOP_(loopstart,loopEnd)>1 which represents that it is permissible toincrease latency of the loops of the DFG if it is needed to minimizebuffering.

FIG. 10 depicts an example workflow 1000 of the compiler 100 of FIG. 1in which examples disclosed herein may be implemented to latency-balanceDFGs for execution on CGRA devices (e.g., the CGRA device 142 of FIG.1). The example compiler 100 includes an example compilation process1002, an example elaboration process 1004, an example buffer insertionprocess 1006, an example fusion process 1008, an example place and routeprocess 1010, and an example request address file (RAF) allocatorprocess 1012. The example processes of the workflow 1000 may beimplemented by one or more logic circuits and/or one or more processors(e.g., the processor 1412 of FIG. 14). While FIG. 10 shows an examplemanner of organizing the example workflow 1000, the example processesdepicted in FIG. 10 can be reordered, one or more of the processes canbe run multiple times in any sequence, one or more of the processes canbe omitted, and/or one or more other processes can be inserted.

If the compiler 100 receives a high-level language program 1016, theexample compilation process 1002 converts the high-level languageprogram 1016 into a low-level language (e.g., assembly language) for theelaboration process 1004. If the compiler 100 receives a low-levellanguage program 1018, the compilation process 1002 is skipped, and theexample elaboration process 1004 directly receives the low-levellanguage program 1018. The example elaboration process 1004 convertslow-level language programs into DFGs (e.g., the input DFG 126 of FIGS.1 and 2A-2C) and generates metadata describing the topology of the DFG.The example buffer insertion process 1006 performs backedge detectionand annotation and performs buffer insertion in accordance withteachings of this disclosure to generate output DFGs (e.g., the outputDFG 132 (FIGS. 1 and 3A-3C). In the illustrated example, the backedgedetector 102 and the buffer inserter 104 of FIG. 1 implement the bufferinsertion process 1006.

The example fusion process 1008 fuses, combines, or joins multiple nodeoperations together on one PE of a target device (e.g., the CGRA device142 of FIG. 1). The example place and route process 1010 loads theoutput DFG 132 to the resources of the target device and routesinterconnections between the resources based on the nodes and connectionarcs of the output DFG 132 to execute the output DFG 132. The exampleRAF allocator process 1012 allocates RAF memory interfaces to resourcesthat need to access memory. In this manner, resources can implementoperations of the output DFG 132 that need to read from memory, write tomemory, copy between memory locations, etc. As shown in FIG. 10, programdirectives such as bandwidth estimates (e.g., issue counts) and loopmembership designations may be provided by the compiler 100 and/or by aprogrammer. When provided by the compiler 100, the compiler 100 obtainsthe directives from input source code and/or generates directives basedon its analysis of the input source code. When provided by a programmer,the programmer provides the directives in a source file 1022.

While an example manner of implementing the backedge detector 102 andthe buffer inserter 104 are illustrated in FIG. 1, one or more of theelements, processes and/or devices illustrated in FIG. 1 may becombined, divided, re-arranged, omitted, eliminated and/or implementedin any other way. Further, the example characteristic detector 106, theexample characteristic comparator 108, the example backedge identifiergenerator 110, the example backedge filter 112, the example latencycalculator 114, the example latency comparator 116, the example bufferallocator 118, the example delay generator 120 and/or, more generally,the example backedge detector 102 and/or the example buffer inserter 104of FIG. 1 may be implemented by hardware, software, firmware and/or anycombination of hardware, software and/or firmware. Thus, for example,any of the example characteristic detector 106, the examplecharacteristic comparator 108, the example backedge identifier generator110, the example backedge filter 112, the example latency calculator114, the example latency comparator 116, the example buffer allocator118, the example delay generator 120 and/or, more generally, the examplebackedge detector 102 and/or the example buffer inserter 104 could beimplemented by one or more analog or digital circuit(s), logic circuits,programmable processor(s), programmable controller(s), graphicsprocessing unit(s) (GPu(s)), digital signal processor(s) (DSP(s)),application specific integrated circuit(s) (ASIC(s)), programmable logicdevice(s) (PLD(s)) and/or field programmable logic device(s) (FPLD(s)).When reading any of the apparatus or system claims of this patent tocover a purely software and/or firmware implementation, at least one ofthe example characteristic detector 106, the example characteristiccomparator 108, the example backedge identifier generator 110, theexample backedge filter 112, the example latency calculator 114, theexample latency comparator 116, the example buffer allocator 118, theexample delay generator 120, the example backedge detector 102, and/orthe example buffer inserter 104 is/are hereby expressly defined toinclude a non-transitory computer readable storage device or storagedisk such as a memory, a digital versatile disk (DVD), a compact disk(CD), a Blu-ray disk, etc. including the software and/or firmware.Further still, the example backedge detector 102 and/or the examplebuffer inserter 104 of FIG. 1 may include one or more elements,processes and/or devices in addition to, or instead of, thoseillustrated in FIG. 1, and/or may include more than one of any or all ofthe illustrated elements, processes and devices. As used herein, thephrase “in communication,” including variations thereof, encompassesdirect communication and/or indirect communication through one or moreintermediary components, and does not require direct physical (e.g.,wired) communication and/or constant communication, but ratheradditionally includes selective communication at periodic intervals,scheduled intervals, aperiodic intervals, and/or one-time events.

In examples disclosed herein, the characteristic detector 106 mayimplement means for storing a node characteristic identifier, thecharacteristic comparator 108 may implement means for comparing a nodecharacteristic identifier with a reference criterion, the backedgeidentifier generator 110 may implement means for generating a backedgeidentifier, the backedge filter 112 may implement means for removing abackedge, the latency calculator 114 may implement means for determininga critical path latency of a critical path of a DFG, the latencycomparator 116 may implement means for comparing a critical path latencyto a latency sum of a buffer latency and a noncritical path latency, thebuffer allocator 118 may implement means for inserting a buffer in apath of a DFG, and the delay generator 120 may implement means forinserting a delay operation in a path of a DFG and/or may implementmeans for decreasing a target data throughput performance of a DFG(e.g., using a SLACK parameter).

Flowcharts representative of example hardware logic, machine readableinstructions, hardware implemented state machines, and/or anycombination thereof for implementing the example backedge detector 102and/or the example buffer inserter 104 of FIG. 1 is shown in FIGS.11-13. The machine readable instructions may be one or more executableprograms or portion(s) of one or more executable programs for executionby a computer processor such as the processor 1412 shown in the exampleprocessor platform 1400 discussed below in connection with FIG. 14. Theprogram(s) may be embodied in software stored on a non-transitorycomputer readable storage medium such as a CD-ROM, a floppy disk, a harddrive, a DVD, a Blu-ray disk, or a memory associated with the processor1412, but the entirety of the program(s) and/or parts thereof couldalternatively be executed by a device other than the processor 1412and/or embodied in firmware or dedicated hardware. Further, although theexample program(s) is/are described with reference to the flowchartsillustrated in FIGS. 11-13, many other methods of implementing theexample backedge detector 102 and/or the example buffer inserter 104 mayalternatively be used. For example, the order of execution of the blocksmay be changed, and/or some of the blocks described may be changed,eliminated, or combined. Additionally or alternatively, any or all ofthe blocks may be implemented by one or more hardware circuits (e.g.,discrete and/or integrated analog and/or digital circuitry, an FPGA, anASIC, a comparator, an operational-amplifier (op-amp), a logic circuit,etc.) structured to perform the corresponding operation withoutexecuting software or firmware.

The machine readable instructions described herein may be stored in oneor more of a compressed format, an encrypted format, a fragmentedformat, a packaged format, etc. Machine readable instructions asdescribed herein may be stored as data (e.g., portions of instructions,code, representations of code, etc.) that may be utilized to create,manufacture, and/or produce machine executable instructions. Forexample, the machine readable instructions may be fragmented and storedon one or more storage devices and/or computing devices (e.g., servers).The machine readable instructions may require one or more ofinstallation, modification, adaptation, updating, combining,supplementing, configuring, decryption, decompression, unpacking,distribution, reassignment, etc. in order to make them directly readableand/or executable by a computing device and/or other machine. Forexample, the machine readable instructions may be stored in multipleparts, which are individually compressed, encrypted, and stored onseparate computing devices, wherein the parts when decrypted,decompressed, and combined form a set of executable instructions thatimplement a program such as that described herein. In another example,the machine readable instructions may be stored in a state in which theymay be read by a computer, but require addition of a library (e.g., adynamic link library (DLL)), a software development kit (SDK), anapplication programming interface (API), etc. in order to execute theinstructions on a particular computing device or other device. Inanother example, the machine readable instructions may need to beconfigured (e.g., settings stored, data input, network addressesrecorded, etc.) before the machine readable instructions and/or thecorresponding program(s) can be executed in whole or in part. Thus, thedisclosed machine readable instructions and/or corresponding program(s)are intended to encompass such machine readable instructions and/orprogram(s) regardless of the particular format or state of the machinereadable instructions and/or program(s) when stored or otherwise at restor in transit.

As mentioned above, the example processes of FIGS. 11-13 may beimplemented using executable instructions (e.g., computer and/or machinereadable instructions) stored on a non-transitory computer and/ormachine readable medium such as a hard disk drive, a flash memory, aread-only memory, a compact disk, a digital versatile disk, a cache, arandom-access memory and/or any other storage device or storage disk inwhich information is stored for any duration (e.g., for extended timeperiods, permanently, for brief instances, for temporarily buffering,and/or for caching of the information). As used herein, the termnon-transitory computer readable medium is expressly defined to includeany type of computer readable storage device and/or storage disk and toexclude propagating signals and to exclude transmission media.

“Including” and “comprising” (and all forms and tenses thereof) are usedherein to be open ended terms. Thus, whenever a claim employs any formof “include” or “comprise” (e.g., comprises, includes, comprising,including, having, etc.) as a preamble or within a claim recitation ofany kind, it is to be understood that additional elements, terms, etc.may be present without falling outside the scope of the correspondingclaim or recitation. As used herein, when the phrase “at least” is usedas the transition term in, for example, a preamble of a claim, it isopen-ended in the same manner as the term “comprising” and “including”are open ended. The term “and/or” when used, for example, in a form suchas A, B, and/or C refers to any combination or subset of A, B, C such as(1) A alone, (2) B alone, (3) C alone, (4) A with B, (5) A with C, (6) Bwith C, and (7) A with B and with C. As used herein in the context ofdescribing structures, components, items, objects and/or things, thephrase “at least one of A and B” is intended to refer to implementationsincluding any of (1) at least one A, (2) at least one B, and (3) atleast one A and at least one B. Similarly, as used herein in the contextof describing structures, components, items, objects and/or things, thephrase “at least one of A or B” is intended to refer to implementationsincluding any of (1) at least one A, (2) at least one B, and (3) atleast one A and at least one B. As used herein in the context ofdescribing the performance or execution of processes, instructions,actions, activities and/or steps, the phrase “at least one of A and B”is intended to refer to implementations including any of (1) at leastone A, (2) at least one B, and (3) at least one A and at least one B.Similarly, as used herein in the context of describing the performanceor execution of processes, instructions, actions, activities and/orsteps, the phrase “at least one of A or B” is intended to refer toimplementations including any of (1) at least one A, (2) at least one B,and (3) at least one A and at least one B.

FIG. 11 is a flowchart representative of example machine-readableinstructions which may be executed to implement the example compiler 100of FIG. 1 to detect and annotate backedges, and insert buffers in DFGsin accordance with teachings of this disclosure. The example flowchartof FIG. 11 includes an example backedge detection and annotation phase1102 and an example buffer insertion phase 1104. In the illustratedexample, the backedge detection and annotation phase 1102 is implementedby the backedge detector 102 of FIG. 1, and the buffer insertion phase1104 is implemented by the buffer inserter 104 of FIG. 1. The examplebackedge detection and annotation phase 1102 and the example bufferinsertion phase 1104 may be implemented by the same program or byseparate programs. In addition, in some examples, the backedge andannotation phase 1102 may be performed without subsequently performingthe example buffer insertion phase 1104. For example, the backedge andannotation phase 1102 may be performed to determine where backedgesexist in an cyclic DFG and/or to remove such backedges to generate anacyclic DFG without subsequently inserting buffers. In some examples,the example buffer insertion phase 1104 may be performed on a DFGwithout performing the backedge and annotation phase 1102 on the DFG.For example, if an input DFG is already acyclic, the backedge andannotation phase 1102 does not need to be performed because the inputacyclic DFG does not have any backedges that need to be removed.

The example program(s) of FIG. 11 begin(s) at block 1106 of the backedgedetection and annotation phase 1102. At block 1106, the example backedgedetector 102 (FIG. 1) detects and annotates backedge(s) in an input DFG(e.g., the input DFG 126 of FIG. 1). For example, the backedge detector102 can analyze the input DFG 126 to identify backedges as describedabove and annotate backedges in the input DFG 126 by storing backedgeidentifiers in association with connection arcs of the input DFG 126 inthe memory 124 (FIG. 1). An example process that may be used toimplement the backedge detection and annotation of block 1106 isdescribed below in connection with FIG. 12.

Turning to the example buffer insertion phase 1104, the backedge filter112 (FIG. 1) accesses backedge annotations from the memory 124 (block1108). The example backedge filter 112 removes backedge(s) based on thebackedge annotations (block 1110). For example, in the input DFG 126,the backedge filter 112 removes backedge(s) between corresponding sourceand sink nodes having connection arc(s) annotated with backedgeidentifier(s) to generate an acyclic DFG as represented by the exampleintermediate DFG 130 of FIG. 1. Although the backedge removal is shownas part of the buffer insertion phase 1104 in FIG. 11, in otherexamples, the backedge removal of blocks 1108 and 1110 may instead beimplemented in the backedge detection and annotation phase 1102. Atblock 1112, the example buffer inserter 104 inserts buffer(s) in theDFG. An example process that may be used to implement the bufferinsertion of block 1112 is described below in connection with FIG. 12.The example process of FIG. 11 ends.

FIG. 12 is a flowchart representative of example machine-readableinstructions which may be executed to implement the example backedgedetector 102 of FIG. 1 to detect and annotate backedges from DFGs. Theexample program of FIG. 12 starts at block 1202 at which thecharacteristic detector 106 (FIG. 1) stores node characteristicidentifier(s) of node(s) in the memory 124 (FIG. 1) association with thenode(s). For example, the characteristic detector 106 analyzes nodes ofthe input DFG 126 using any suitable technique including the exampleDFS-based techniques described above, the BFS technique described above,the post-order traversal and dominator analysis technique describedabove, the manual backedge annotation technique described above, or anyother suitable technique, and stores corresponding node characteristicidentifier(s) in association with the nodes.

In examples in which the backedge detector 102 uses a DFS-based nodeanalysis technique, the characteristic detector 106 sets characteristicidentifiers for the nodes of the input DFG 126 for multiple logicalclock cycles of the DFG 126 such that each node of the DFG 126 isassigned multiple characteristic identifiers for different executioncycles from the start of execution of the DFG 126 through completion ofexecution of the DFG 126. In the DFS-based node analysis technique, anode characteristic identifier is settable to: (a) an unexecuted-statusidentifier to indicate a node has not yet been executed during executionof the DFG, (b) an executing-status identifier indicative of a nodebeing executing during a current logical clock cycle of the DFG, and (c)a completed-status identifier to indicate that no further executions ofa node are to occur during execution of the DFG.

In examples in which the backedge detector 102 uses a BFS-based nodeanalysis technique, the characteristic detector 106 sets characteristicidentifiers for the nodes of the input DFG 126 based on their executiondepth level in the DFG 126 as described above. In other examples thatare not DFS-based or BFS-based node analysis techniques, thecharacteristic detector 106 sets characteristic identifiers for thenodes using any identification suitable for identifying nodes at whichbackedges occur.

The example characteristic comparator 108 (FIG. 1) compares a nodecharacteristic identifier of a node to reference criterion (block 1204).For example, the characteristic comparator 108 compares the nodecharacteristic identifier of the node o2 of FIGS. 1, 2A-2C, and 3A-3C toa reference criterion to determine whether a backedge connects to thenode o2. In the DFS-based node analysis technique, the referencecriterion is an executing-status identifier, and the characteristiccomparator 108 is to confirm a presence of the backedge at the node o2when the node characteristic identifier of the node o2 matches theexecuting-status identifier during two logical clock cycles. That is,during a first logical clock cycle at which the node o2 is firstattributed with the executing-status identifier, the characteristiccomparator 108 does not confirm a backedge because no nodecharacteristic identifier for the node o2 for a prior logical clockcycle matches the executing-status identifier. However, when the nodecharacteristic identifier for the node o2 is the executing-statusidentifier at a subsequent logical clock cycle, the characteristiccomparator 108 confirms a backedge based on confirming a match betweenthe executing-status identifier of the node o2 during the subsequentlogical clock cycle and the executing-status identifier of the node o2during a previous logical clock cycle. In such examples, the referencecriterion is the executing-status identifier attributed to the node o2during the subsequent logical clock cycle.

In the BFS-based node analysis technique, the reference criterion is adepth level identifier of a source node of an edge. For example, withreference to the input DFG 126 of FIG. 2C, the node characteristicidentifier of the node o2 (e.g., a sink node relative to the node o5along the backedge 128) is a lower depth level identifier, and thereference criterion used by the characteristic comparator 108 is ahigher depth level of the node o5 (e.g., a source node relative to thenode o2 along the backedge 128). The example characteristic comparator108 confirms a presence of a backedge based on execution control of theDFG 126 returning from the higher depth level of the node o5 to thelower depth level of the node o2.

When the characteristic comparator 108 confirms a backedge (block 1206),the example backedge identifier generator 110 (FIG. 1) annotates abackedge (block 1208). For example, the backedge identifier generator110 generates a backedge identifier indicative of a backedge at aconnection arc between source and sink nodes of the DFG 126. The examplebackedge identifier generator 110 can store the backedge identifier inthe memory 124 in association with the connection arc between the sourceand sink nodes.

After annotating the backedge at block 1208, or if the characteristiccomparator 108 determines at block 1206 that a backedge is notconfirmed, the backedge detector 102 determines whether there is anothernode to analyze (block 1210). If there is another node of the DFG 126 toanalyze, control returns to block 1204. Otherwise, the process of FIG.12 ends. In addition, control may return to a calling function orprocess such as the example process of FIG. 11.

FIG. 13 is a flowchart representative of machine-readable instructionswhich may be executed to implement the example buffer inserter 104 ofFIG. 1 to insert buffers in noncritical paths of DFGs without exceedingcritical path latencies of the DFGs. The program of FIG. 13 begins atblock 1302 at which the example latency calculator 114 (FIG. 1)determines a critical path latency of a DFG. For example, the latencycalculator 114 determines the critical path latency of the critical path204 (FIG. 2A) of the intermediate DFG 130 that includes a loop startnode (e.g., the second node o2) and a loop end node (e.g., the fifthnode o5) from which a backedge was removed at block 1110 of FIG. 11. Insuch example, the loop start node receives input data, and the loop endnode generates output data associated with the input data of the loopstart node because the loop start node is an ancestor of the loop endnode along the same edge of the intermediate DFG 130. At block 1304, theexample latency comparator 116 (FIG. 1) compares the critical pathlatency to a latency sum of a buffer latency and a noncritical pathlatency. For example, the noncritical path latency is the latency of thenoncritical path 202 of FIG. 2A. As described above, in examplesdisclosed herein, a latency sum of a path can also be referred to as acapacity sum of that path. A capacity sum of a path or edge is at leastas large as its latency sum because the capacity should be large enoughto tolerate the latency (or buffers) in that path. The example latencycomparator 116 may perform the comparison of block 1304 in accordancewith Constraint 1, Constraint 4, and/or Constraint 5 described above.

If the example latency comparator 116 determines at block 1306 that thelatency sum (or capacity sum) is less than or equal to the critical pathlatency, the example buffer allocator 118 (FIG. 1) inserts a buffer inthe noncritical path 202 (block 1308). In other examples, the latencysum comparison and analysis of blocks 1304 and 1306 can be based oninserting multiple buffers into a noncritical path simultaneously (e.g.,instead of inserting only one buffer at a time). In such examples, thebuffer insertion operation of block 1308 is to insert the same number ofmultiple buffers as involved in the analysis operations of blocks 1304and 1306.

After the buffer insertion of block 1308 or if the latency comparator116 determines at block 1306 that the latency sum is not less than orequal to the critical path latency, the latency comparator 116determines whether the DFG is substantially latency-balanced (block1310). For example, the latency comparator 116 may determine that theDFG is substantially latency-balanced when it performs a comparison thecritical path latency and the buffered noncritical path latency and thecomparison indicates a difference of less than one buffer latency. Ifthe latency comparator 116 determines at block 1310 that the DFG is notlatency balanced, the buffer allocator 118 determines whether allbuffers available in a target device have been allocated (block 1312).The buffer allocator 118 may determine whether all buffers available inthe target device have been allocated based on Constraint 6 above. Forexample, if the buffer allocation has not reached the maximum storageboxes available in the target CGRA device 142 (FIG. 1), control returnsto block 1304 to perform another buffer insertion analysis (e.g., if anyremaining latency constraints are not satisfied).

If the buffer allocator 118 determines at block 1312 that all buffershave been allocated, the delay generator 120 (FIG. 2) performs a SLACKadjustment (block 1314). For example, the delay generator 120 performs aSLACK adjustment as described above in connection with Constraint 3 tofacilitate latency-balancing the DFG by decreasing a target datathroughput to be less than one when insufficient buffers are availableon a target device (e.g., the CGRA device 142 of FIG. 1). In examplesdisclosed herein, slackening at block 1314 can be performed on andapplied to all edges uniformly so that all edges of a DFG have the samedata throughput (e.g., the throughput of each edge of the DFG ismultiplied by the same SLACK multiplier so that the whole DFG isuniformly slackened), or slackening can be performed on a per-edge basissuch that data throughput can be modulated differently for differentedges of the DFG. After performing the SLACK adjustment at block 1314,control returns to block 1304 to restart the buffer insertion processbased on the lower target data throughput. In some examples, the delaygenerator 120 may additionally or alternatively insert a delay operationin the noncritical path 202 when the buffer allocator 118 determinesthat another buffer is not available for insertion in the noncriticalpath 202 to increase a similarity between the critical path latency andthe noncritical path latency. When the latency comparator 116 determinesat block 1310 that the DFG is latency-balanced, the process of FIG. 13ends. In addition, control may return to a calling function or processsuch as the example process of FIG. 11.

FIG. 14 is a block diagram of an example processing platform 1400structured to execute the instructions of FIGS. 11-13 to implement theexample compiler 100 of FIG. 1, the example backedge detector 102 ofFIG. 1, and/or the example buffer inserter 104 of FIG. 1. The processorplatform 1400 can be, for example, a server, a personal computer, aworkstation, a self-learning machine (e.g., a neural network), or anyother suitable type of computing device.

The processor platform 1400 of the illustrated example includes aprocessor 1412. The processor 1412 of the illustrated example ishardware. For example, the processor 1412 can be implemented by one ormore integrated circuits, logic circuits, microprocessors, GPus, DSPs,or controllers from any desired family or manufacturer. The hardwareprocessor 1412 may be a semiconductor based (e.g., silicon based)device. In this example, the processor 1412 implements the examplecompiler 100, the example backedge detector 102, the example bufferinserter 104, the example characteristic detector 106, the examplecharacteristic comparator 108, the example backedge identifier generator110, the example backedge filter 112, the example latency calculator114, the example latency comparator 116, the example buffer allocator118, and the example delay generator 120.

The processor 1412 of the illustrated example includes a local memory1413 (e.g., a cache). The processor 1412 of the illustrated example isin communication with a main memory including a volatile memory 1414 anda non-volatile memory 1416 via a bus 1418. The volatile memory 1414 maybe implemented by Synchronous Dynamic Random Access Memory (SDRAM),Dynamic Random Access Memory (DRAM), RAMBUS® Dynamic Random AccessMemory (RDRAM®) and/or any other type of random access memory device.The non-volatile memory 1416 may be implemented by flash memory and/orany other desired type of memory device. Access to the main memory 1414,1416 is controlled by a memory controller.

The processor platform 1400 of the illustrated example also includes aninterface circuit 1420. The interface circuit 1420 may be implemented byany type of interface standard, such as an Ethernet interface, auniversal serial bus (USB), a Bluetooth® interface, a near fieldcommunication (NFC) interface, and/or a PCI express interface.

In the illustrated example, one or more input devices 1422 are connectedto the interface circuit 1420. The input device(s) 1422 permit(s) a userto enter data and/or commands into the processor 1412. The inputdevice(s) can be implemented by, for example, an audio sensor, amicrophone, a camera (still or video), a keyboard, a button, a mouse, atouchscreen, a track-pad, a trackball, isopoint and/or a voicerecognition system.

One or more output devices 1424 are also connected to the interfacecircuit 1420 of the illustrated example. The output devices 1424 can beimplemented, for example, by display devices (e.g., a light emittingdiode (LED), an organic light emitting diode (OLED), a liquid crystaldisplay (LCD), a cathode ray tube display (CRT), an in-place switching(IPS) display, a touchscreen, etc.), a tactile output device, a printerand/or speaker. The interface circuit 1420 of the illustrated example,thus, typically includes a graphics driver card, a graphics driver chipand/or a graphics driver processor.

The interface circuit 1420 of the illustrated example also includes acommunication device such as a transmitter, a receiver, a transceiver, amodem, a residential gateway, a wireless access point, and/or a networkinterface to facilitate exchange of data with external machines (e.g.,computing devices of any kind) via a network 1426. The communication canbe via, for example, an Ethernet connection, a digital subscriber line(DSL) connection, a telephone line connection, a coaxial cable system, asatellite system, a line-of-site wireless system, a cellular telephonesystem, etc.

The processor platform 1400 of the illustrated example also includes oneor more mass storage devices 1428 for storing software and/or data.Examples of such mass storage devices 1428 include floppy disk drives,hard drive disks, compact disk drives, Blu-ray disk drives, redundantarray of independent disks (RAID) systems, and digital versatile disk(DVD) drives.

Machine executable instructions 1432 represented by the flowcharts ofFIGS. 11-13 may be stored in the mass storage device 1428, in thevolatile memory 1414, in the non-volatile memory 1416, and/or on aremovable non-transitory computer readable storage medium such as a CDor DVD.

FIG. 15 depicts an example array of processing elements (PEs) 1500 of aCGRA device (e.g., the CGRA device 142 of FIG. 1). The example array ofPEs 1500 may be programmed to execute DFGs such as the input DFG 126(FIGS. 1 and 2A-2C) and/or the output DFG 132 (FIGS. 1 and 3A-3C). Theexample array of PEs 1500 is a heterogenous array in that the PEs aredifferent types of hardware circuits (e.g., logic circuits and/or analogcircuits) structured to perform different types of operations of nodesof a DFG. The example array of PEs 1500 may be fabricated on one or moresemiconductor substrates. In the example of FIG. 15, ones of the PEsdenoted by the letter CA′ are integer arithmetic PEs structured toperform operations involving integer calculations, ones of the PEsdenoted by the letters ‘FP’ are floating point arithmetic PEs structuredto perform operations involving floating point calculations, ones of thePEs denoted by the letter ‘C’ are communication PEs structured toperform communication operations to send/receive data within and/orexternal to the array of PEs 1500, and ones of the PEs denoted by theletter CS' are in-fabric storage PEs (e.g., RAM, SRAM, DRAM, etc.) thatimplement storage boxes. For example, the in-fabric storage PEsimplement buffers inserted in DFGs by the buffer inserter 104 inaccordance with teachings of this disclosure.

To access memory and/or cache of a CGRA device, the array of PEs 1500 isprovided with an example request address file (RAF) memory interface1502. For example, the RAF memory interface 1502 may be used by the PEsto read external input data into nodes in a DFG from memory and/or cacheand/or to write external output data from nodes of the DFG to memoryand/or cache. The PEs are connected to one another via in-fabric databuses or channels as shown in FIG. 16 in an enlarged view of the examplearray of PEs 1500. To configure the PEs to execute a DFG, the place androute process 1010 of FIG. 10 loads or writes code representing the DFGinto the array of PEs 1500 to program different types of the PEscorresponding to the different types of operations of the DFG.Producer-consumer paths are routed between the PEs based on thein-fabric data buses or channels shown in FIG. 16. Although only asingle array of PEs 1500 is shown in FIG. 15, a CGRA device can beprovided with multiple arrays of PEs substantially similar to the arrayof PEs 1500. Multiple interconnected arrays of PEs may be fabricated onone or more semiconductor substrates.

Additional details of CGRA devices (e.g., CSA devices) are disclosed inU.S. patent application Ser. No. 15/396,402, filed Dec. 30, 2016, andentitled “Processors, Methods, and Systems with a Configurable SpatialAccelerator.” U.S. patent application Ser. No. 15/396,402 isincorporated herein by reference in its entirety. Although examplesdisclosed herein are described in connection with CGRA devices, examplesdisclosed herein may additionally or alternatively be implemented inconnection with other types of devices such as FPGA devices, differenttypes of CGRA architectures, etc.

From the foregoing, it will be appreciated that example methods,apparatus and articles of manufacture have been disclosed that may beused to implement a DFG performance optimization feature of a complier(e.g., the compiler 100 of FIG. 1) to improve throughput performance ofDFGs. For example, to improve throughput performance of DFGs, examplesdisclosed herein adjust path latencies of noncritical paths to match orbe substantially similar to the longest path latency (e.g., a criticalpath latency) of a DFG by inserting buffers in the noncritical paths.The disclosed methods, apparatus and articles of manufacture areaccordingly directed to one or more improvement(s) in the functioning ofa computer.

Although prior techniques provide buffer insertion solutions forsynchronous dataflow architectures, examples disclosed herein are usefulfor inserting buffers in DFGs that run on asynchronous CGRA devices. Forexample, a prior technique by Gao Guang Rong (“Gao's algorithm”) seeksto buffer a synchronous acyclic DFG. (Gao's algorithm is described in apaper entitled, “A Pipelined Code Mapping Scheme for Static Data FlowComputers,” Massachusetts Institute of Technology, Aug. 28, 1986.)However, Gao's algorithm assumes an unlimited supply of buffering andthen tries to minimize buffering in a way that does not increase thecritical path latency and constructs final silicon to match bufferingrequirements. Examples disclosed herein overcome physical constraints ofCGRA device chips in which buffer storage is limited. As such, examplesdisclosed herein are useful to optimize latency while generating anacceptable reduced-performance solution when the limited buffer storageis exhausted. Examples disclosed herein also enable relaxing thecritical path latency constraint to be able to fit limited budgetsbuffer resources while minimizing the overall increase in the criticalpath latency.

In addition, Gao's algorithm only works for synchronous DFGs that do nothave cycles (e.g., directed acyclic graphs). However, many real-worldDFGs do contain cycles, especially if there is a while loop or loopswith arbitrarily complex inner loop dependency pattern. Therefore,examples disclosed herein are significantly more useful than priortechniques because they latency-balance DFGs that contain cycles. Inaddition, examples disclosed herein target DFGs that are more complex(e.g., DFGs that contain one or more cycles) than DFGs that can beprocessed using Gao's algorithm.

In addition, Gao's algorithm assumes a uniform data-rate of 1 andtargets a synchronous dataflow architecture. However, examples disclosedherein can be applied to asynchronous dataflow architecture in whicheach operation can have a variable data rate throughput. Gao's algorithmonly works for directed acyclic DFGs. However, examples disclosed hereinhandle buffer insertion for arbitrary DFGs that may contain cycles orloops.

Examples disclosed herein also consider a fundamentally asynchronousarchitecture in which the amount of buffering is not necessarilyequivalent to the latency of the buffering. However, the prior techniqueof Gao's algorithm assumes latency is equivalent to buffering, whichmeans if there is one buffer, then that will allow tolerating one unitof latency. In contrast, in DFG structures that may be latency-balancedusing examples disclosed herein, buffering is elastic instead of beinglinear. That is, in examples disclosed herein, changes in latency arenot directly related to changes in capacity/buffering. Some examplesdisclosed herein insert buffers only in certain discrete sizes (e.g., asize defined by capacity ‘C’). Such discrete-size storage boxesimplement the buffers (e.g., buffer boxes) for insertion in DFGs inaccordance with teachings of this disclosure. Each buffer box has amaximum capacity of C and adds a constant latency of k≤C cycles at thepoint of insertion. The prior technique of Gao's algorithm assumesbuffers can be of any arbitrary size and does not have any limit oftotal buffers being used. Therefore, Gao's algorithm cannot be directlyapplied to solve a latency-balancing problem intended to a practicalsolution for executing a DFG on real hardware.

In addition, each connection arc or interconnect in a target CGRA device(e.g., the CGRA device 142 of FIG. 1) has some predetermined constant Ccapacity. The prior technique of Gao's algorithm does not account forthe pre-existing capacity. Thus, it would be pessimistic and aninefficient use of hardware resources to use Gao's algorithm “as is”because it would require inserting more buffers than actually needed.Also, unlike the prior technique of Gao's algorithm, latency-balancingthrough buffer insertion using examples disclosed herein can be used toincrease data throughput performance of a DFG even if such buffering isnot necessary to correctly execute the DFG.

Example Performance Results

Examples disclosed herein were tested in a controlled laboratoryenvironment. In particular, the example buffer insertion techniquesdisclosed herein were implemented using python with networkx and somesupplemental linear programming libraries. The input DFG to the examplesdisclosed herein was a binary search abstract DFG which included severalcycles. After creating a graphical representation of the DFG, examplesdisclosed herein detected, annotated, and removed backedges from theDFG, and created equations to represent the DFG structure, and performedthe buffer insertion process in accordance with teachings of thisdisclosure based on a linear programming solver from cvxpy with a goalto minimize buffers. The output DFG program was run on an Intel CSAdevice (e.g., a CGRA device) using its cycle-accurate simulator usingthe following configurations.

Unrealistic default: All edges have a default quantity of 128 storageboxes

Realistic default without BI: All edges have a default depth of three,except 1-bit edges which have a default depth of eight (Buffer Insertionis not used).

Realistic default with BI: All edges have a default depth of three,except 1-bit edges which have a default depth of eight (Buffer Insertionis used).

The test implementation assumed that a maximum of 512 storage boxes,each with a capacity of 32 bits.

Table 3 below shows that the buffer insertion techniques disclosedherein were able to insert buffers in the cyclic DFG and match theunrealistic default performance bound.

TABLE 3 Buffer Insertion in Matching Unrealistic Default PerformanceBound Realistic Unrealistic default Realistic Statistics default withoutBI default with BI Cycles 66998 710212 66634 Buffer boxes 14 14 31 + 14(pre-existing) (pre-existing) #Edges where 7 7 18 + 7  buffers added

Similar improved trends were observed for other computer kernels. Forexample, FIG. 17 is an example comparative bar graph comparing storageboxes used by an automatic buffer insertion (ABI) process implemented inaccordance with teachings of this disclosure when throughput is used asa constraint to the buffer insertion process and when throughput is notused as a constraint to the buffer insertion process. In addition, FIG.18 is an example comparative bar graph comparing performance of apractical dataflow graph to a dataflow graph with unpractically deep 128depth buffers in all interconnecting arcs (e.g., for all edges) when anABI process implemented in accordance with teachings of this disclosureuses throughput as a constraint and when throughput is not used as aconstraint. These results show that example buffer insertion techniquesdisclosed herein achieve performance close to the 128 buffer depth for anumber of other workloads. The results also show that use of throughputas a constraint reduces the number of buffer boxes significantly in somecases.

The following pertain to further examples disclosed herein.

Example 1 is an apparatus to insert buffers in a dataflow graph. Theapparatus of Example 1 includes a backedge filter to remove a backedgebetween a first node and a second node of the dataflow graph, the firstnode representing a first operation of the dataflow graph, the secondnode representing a second operation of the dataflow graph; a latencycalculator to determine a critical path latency of a critical path ofthe dataflow graph that includes the first node and the second node, thecritical path having a longer latency to completion relative to a secondpath that terminates at the second node; a latency comparator to comparethe critical path latency to a latency sum of a buffer latency and asecond path latency, the second path latency corresponding to the secondpath; and a buffer allocator to insert one or more buffers in the secondpath based on the comparison performed by the latency comparator.

In Example 2, the subject matter of Example 1 can optionally includethat the first node is a source node that generates an output, and thesecond node is a sink node that executes after the source node andconsumes an input.

In Example 3, the subject matter of any one of Examples 1-2 canoptionally include that the first node receives input data, and thesecond node generates output data associated with the input data.

In Example 4, the subject matter of any one of Examples 1-3 canoptionally include that the critical path latency is based on having alatency sum greater than the second path latency.

In Example 5, the subject matter of any one of Examples 1-4 canoptionally include that the latency comparator is to compare thecritical path latency to a second latency sum of the buffer latency, thesecond path latency, and a second buffer latency; and the bufferallocator is to not insert a second buffer in the second path when thelatency comparator determines that the second latency sum exceeds thecritical path latency.

In Example 6, the subject matter of any one of Examples 1-5 canoptionally include that the backedge forms a loop with the criticalpath, and the backedge filter is to remove the backedge based on abackedge identifier stored in memory in association with a connectionarc between the first node and the second node.

In Example 7, the subject matter of any one of Examples 1-6 canoptionally include that the buffer is a storage box in a coarse-grainreconfigurable architecture, and the buffer latency corresponds to alogical clock cycle.

In Example 8, the subject matter of any one of Examples 1-7 canoptionally include a delay generator to insert a delay operation in thesecond path when the buffer allocator determines that a second buffer isnot available in a target device for insertion in the second path toincrease a similarity between the critical path latency and the secondpath latency.

In Example 9, the subject matter of any one of Examples 1-8 canoptionally include a delay generator to decrease a target datathroughput performance of the dataflow graph using a SLACK parameterwhen a sufficient number of buffers are not available in a target devicefor insertion in the second path.

In Example 10, the subject matter of any one of Examples 1-9 canoptionally include a delay generator to determine a latency on thesecond path between the first and second nodes by multiplying amultiplier with a throughput of the second path.

In Example 11, the subject matter of any one of Examples 1-10 canoptionally include that a number of the one or more buffers inserted inthe second path does not exceed a capacity of total buffers available ona target device for the second path.

Example 12 is a non-transitory computer readable storage mediumcomprising instructions that, when executed by a processor, cause theprocessor to at least: remove a backedge between a first node and asecond node of a dataflow graph, the first node representing a firstoperation of the dataflow graph, the second node representing a secondoperation of the dataflow graph; determine a critical path latency of acritical path of the dataflow graph that includes the first node and thesecond node, the critical path having a longer latency to completionrelative to a second path that terminates at the second node; comparethe critical path latency to a latency sum of a buffer latency and asecond path latency, the second path latency corresponding to the secondpath; and insert one or more buffers in the second path based on thecomparison performed by the latency comparator.

In Example 13, the subject matter of Example 12 can optionally includethat the first node is a source node that generates an output, and thesecond node is a sink node that executes after the source node andconsumes an input.

In Example 14, the subject matter of any one of Examples 12-13 canoptionally include that the first node receives input data, and thesecond node generates output data associated with the input data.

In Example 15, the subject matter of any one of Examples 12-14 canoptionally include that the critical path latency is based on having alatency sum greater than the second path latency.

In Example 16, the subject matter of any one of Examples 12-15 canoptionally include that the instructions, when executed by theprocessor, are to cause the processor to: compare the critical pathlatency to a second latency sum of the buffer latency, the second pathlatency, and a second buffer latency; and determine to not insert asecond buffer in the second path when the second latency sum exceeds thecritical path latency.

In Example 17, the subject matter of any one of Examples 12-16 canoptionally include that the backedge forms a loop with the criticalpath, and the instructions, when executed by the processor, are to causethe processor to remove the backedge based on a backedge identifierstored in memory in association with a connection arc between the firstnode and the second node.

In Example 18, the subject matter of any one of Examples 12-17 canoptionally include that the buffer is a storage box in a coarse-grainreconfigurable architecture, and the buffer latency corresponds to alogical clock cycle.

In Example 19, the subject matter of any one of Examples 12-18 canoptionally include that the instructions, when executed by theprocessor, are to cause the processor to insert a delay operation in thesecond path when the buffer allocator determines that a second buffer isnot available in a target device for insertion in the second path toincrease a similarity between the critical path latency and the secondpath latency.

In Example 20, the subject matter of any one of Examples 12-19 canoptionally include that the instructions, when executed by theprocessor, are to cause the processor to decrease a target datathroughput performance of the dataflow graph using a SLACK parameterwhen a sufficient number of buffers are not available in a target devicefor insertion in the second path.

In Example 21, the subject matter of any one of Examples 12-20 canoptionally include that the instructions, when executed by theprocessor, are to cause the processor to determine a latency on thesecond path between the first and second nodes by multiplying amultiplier with a throughput of the second path.

In Example 22, the subject matter of any one of Examples 12-21 canoptionally include that a number of the one or more buffers inserted inthe second path does not exceed a capacity of total buffers available ona target device for the second path.

Example 23 is a method to insert buffers in a dataflow graph. The methodof Example 23 includes removing a backedge between a first node and asecond node of the dataflow graph, the first node representing a firstoperation of the dataflow graph, the second node representing a secondoperation of the dataflow graph; determining a critical path latency ofa critical path of the dataflow graph that includes the first node andthe second node, the critical path having a longer latency to completionrelative to a second path that terminates at the second node; comparingthe critical path latency to a latency sum of a buffer latency and asecond path latency, the second path latency corresponding to the secondpath; and inserting one or more buffers in the second path based on thecomparison performed by the latency comparator.

In Example 24, the subject matter of Example 23 can optionally includethat the first node is a source node that generates an output, and thesecond node is a sink node that executes after the source node andconsumes an input.

In Example 25, the subject matter of any one of Examples 23-24 canoptionally include that the first node receives input data, and thesecond node generates output data associated with the input data.

In Example 26, the subject matter of any one of Examples 23-25 canoptionally include that the critical path latency is based on having alatency sum greater than the second path latency.

In Example 27, the subject matter of any one of Examples 23-26 canoptionally include: comparing the critical path latency to a secondlatency sum of the buffer latency, the second path latency, and a secondbuffer latency; and determining to not insert a second buffer in thesecond path when the second latency sum exceeds the critical pathlatency.

In Example 28, the subject matter of any one of Examples 23-27 canoptionally include that the backedge forms a loop with the criticalpath, and further include removing the backedge based on a backedgeidentifier stored in memory in association with a connection arc betweenthe first node and the second node.

In Example 29, the subject matter of any one of Examples 23-28 canoptionally include that the buffer is a storage box in a coarse-grainreconfigurable architecture, and the buffer latency corresponds to alogical clock cycle.

In Example 30, the subject matter of any one of Examples 23-29 canoptionally include inserting a delay operation in the second path whenthe buffer allocator determines that a second buffer is not available ina target device for insertion in the second path to increase asimilarity between the critical path latency and the second pathlatency.

In Example 31, the subject matter of any one of Examples 23-30 canoptionally include decreasing a target data throughput performance ofthe dataflow graph using a SLACK parameter when a sufficient number ofbuffers are not available in a target device for insertion in the secondpath.

In Example 32, the subject matter of any one of Examples 23-31 canoptionally include determining a latency on the second path between thefirst and second nodes by multiplying a multiplier with a throughput ofthe second path.

In Example 33, the subject matter of any one of Examples 23-32 canoptionally include that a number of the one or more buffers inserted inthe second path does not exceed a capacity of total buffers available ona target device for the second path.

Example 34 is an apparatus to insert buffers in a dataflow graph. Theapparatus of Example 34 includes means for removing a backedge between afirst node and a second node of the dataflow graph, the first noderepresenting a first operation of the dataflow graph, the second noderepresenting a second operation of the dataflow graph; means fordetermining a critical path latency of a critical path of the dataflowgraph that includes the first node and the second node, the criticalpath having a longer latency to completion relative to a second paththat terminates at the second node; means for comparing the criticalpath latency to a latency sum of a buffer latency and a second pathlatency, the second path latency corresponding to the second path; andmeans for inserting one or more buffers in the second path based on thecomparison performed by the latency comparator.

In Example 35, the subject matter of Example 34 can optionally includethat the first node is a source node that generates an output, and thesecond node is a sink node that executes after the source node andconsumes an input.

In Example 36, the subject matter of any one of Examples 34-35 canoptionally include that the first node receives input data, and thesecond node generates output data associated with the input data.

In Example 37, the subject matter of any one of Examples 34-36 canoptionally include that the critical path latency is based on having alatency sum greater than the second path latency.

In Example 38, the subject matter of any one of Examples 34-37 canoptionally include that the means for comparing the critical pathlatency is to: compare the critical path latency to a second latency sumof the buffer latency, the second path latency, and a second bufferlatency; and determine not to insert a second buffer in the second pathwhen the latency comparator determines that the second latency sumexceeds the critical path latency.

In Example 39, the subject matter of any one of Examples 34-38 canoptionally include that the backedge forms a loop with the criticalpath, and the means for removing the backedge is to remove the backedgebased on a backedge identifier stored in memory in association with aconnection arc between the first node and the second node.

In Example 40, the subject matter of any one of Examples 34-39 canoptionally include that the buffer is a storage box in a coarse-grainreconfigurable architecture, and the buffer latency corresponds to alogical clock cycle.

In Example 41, the subject matter of any one of Examples 34-40 canoptionally include means for inserting a delay operation in the secondpath when the buffer allocator determines that a second buffer is notavailable in a target device for insertion in the second path toincrease a similarity between the critical path latency and the secondpath latency.

In Example 42, the subject matter of any one of Examples 34-41 canoptionally include means for decreasing a target data throughputperformance of the dataflow graph using a SLACK parameter when asufficient number of buffers are not available in a target device forinsertion in the second path.

In Example 43, the subject matter of any one of Examples 34-42 canoptionally include means for decreasing a target data throughput todetermine a latency on the second path between the first and secondnodes by multiplying a multiplier with a throughput of the second path.

In Example 44, the subject matter of any one of Examples 34-43 canoptionally include that a number of the one or more buffers inserted inthe second path does not exceed a capacity of total buffers available ona target device for the second path.

Example 45 is an apparatus to annotate back edges in a dataflow graph.The apparatus of Example 45 includes a characteristic detector to storea node characteristic identifier in memory in association with a firstnode of the dataflow graph; a characteristic comparator to compare thenode characteristic identifier with a reference criterion; and abackedge identifier generator to generate a backedge identifierindicative of a backedge between the first node and a second node of thedataflow graph based on the comparison, the memory to store the backedgeidentifier in association with a connection arc between the first andsecond nodes.

In Example 46, the subject matter of Example 45 can optionally includethat the reference criterion is an executing-status identifier, and thecharacteristic comparator is to confirm a presence of the backedgebetween the first and second nodes when the node characteristicidentifier matches the executing-status identifier, the executing-statusidentifier indicative of the first node executing during a first logicalclock cycle of the dataflow graph, and the characteristic comparator tocompare the node characteristic identifier with the reference criterioncorresponding to a second logical clock cycle of the dataflow graph.

In Example 47, the subject matter of any one of Examples 45-46 canoptionally include that the node characteristic identifier is settableto: (a) an unexecuted-status identifier to indicate the first node hasnot yet been executed during execution of the dataflow graph, (b) theexecuting-status identifier, and (c) a completed-status identifier toindicate that no further executions of the first node are to occurduring execution of the dataflow graph.

In Example 48, the subject matter of any one of Examples 45-47 canoptionally include that the node characteristic identifier is a firstdepth level identifier of the first node, the reference criterion is asecond depth level identifier of the second node, the characteristiccomparator is to confirm a presence of the backedge based on executioncontrol returning from a higher depth level corresponding to the seconddepth level identifier of the second node to a lower depth levelcorresponding to the first depth level identifier of the first node.

In Example 49, the subject matter of any one of Examples 45-48 canoptionally include that the coarse-grain reconfigurable architecturedevice includes an array of processing elements interconnected by anetwork, the first node to be executed by a first one of the processingelements, and the second node to be executed by a second one of theprocessing elements.

In Example 50, the subject matter of any one of Examples 45-49 canoptionally include that the characteristic detector, the characteristiccomparator, and the backedge identifier generator are to operate inassociation with a compiler, the compiler to generate the dataflow graphbased on source code in at least one of a high-level programminglanguage or assembly programming language.

In Example 51, the subject matter of any one of Examples 45-50 canoptionally include that the backedge identifier generator is to generatethe backedge identifier as a backedge attribute and to store thebackedge attribute in assembly code of the dataflow graph to representthe backedge in the assembly code.

Example 52 is a non-transitory computer readable storage mediumcomprising instructions that, when executed by a processor, cause theprocessor to at least: store a node characteristic identifier in memoryin association with a first node of the dataflow graph; compare the nodecharacteristic identifier with a reference criterion; and generate abackedge identifier indicative of a backedge between the first node anda second node of the dataflow graph based on the comparison, the memoryto store the backedge identifier in association with a connection arcbetween the first and second nodes.

In Example 53, the subject matter of Example 52 can optionally includethat the reference criterion is an executing-status identifier, and theinstructions, when executed by the processor, are to cause the processorto: confirm a presence of the backedge between the first and secondnodes when the node characteristic identifier matches theexecuting-status identifier, the executing-status identifier indicativeof the first node executing during a first logical clock cycle of thedataflow graph; and compare the node characteristic identifier with thereference criterion corresponding to a second logical clock cycle of thedataflow graph.

In Example 54, the subject matter of any one of Examples 52-53 canoptionally include that the node characteristic identifier is settableto: (a) an unexecuted-status identifier to indicate the first node hasnot yet been executed during execution of the dataflow graph, (b) theexecuting-status identifier, and (c) a completed-status identifier toindicate that no further executions of the first node are to occurduring execution of the dataflow graph.

In Example 55, the subject matter of any one of Examples 52-54 canoptionally include that the node characteristic identifier is a firstdepth level identifier of the first node, the reference criterion is asecond depth level identifier of the second node, the instructions, whenexecuted by the processor, are to cause the processor to confirm apresence of the backedge based on execution control returning from ahigher depth level corresponding to the second depth level identifier ofthe second node to a lower depth level corresponding to the first depthlevel identifier of the first node.

In Example 56, the subject matter of any one of Examples 52-55 canoptionally include that the coarse-grain reconfigurable architecturedevice includes an array of processing elements interconnected by anetwork, the first node to be executed by a first one of the processingelements, and the second node to be executed by a second one of theprocessing elements.

In Example 57, the subject matter of any one of Examples 52-56 canoptionally include that the instructions are to be executed inassociation with a compiler, the compiler to generate the dataflow graphbased on source code in at least one of a high-level programminglanguage or assembly programming language.

In Example 58, the subject matter of any one of Examples 52-57 canoptionally include that the instructions, when executed by theprocessor, are to cause the processor to generate the backedgeidentifier as a backedge attribute and to store the backedge attributein assembly code of the dataflow graph to represent the backedge in theassembly code.

Example 59 is a method to annotate back edges in a dataflow graph. Themethod of Example 59 includes storing a node characteristic identifierin memory in association with a first node of the dataflow graph;comparing the node characteristic identifier with a reference criterion;and generating a backedge identifier indicative of a backedge betweenthe first node and a second node of the dataflow graph based on thecomparison, the memory to store the backedge identifier in associationwith a connection arc between the first and second nodes.

In Example 60, the subject matter of Example 59 can optionally includethat the reference criterion is an executing-status identifier, andfurther include: confirming a presence of the backedge between the firstand second nodes when the node characteristic identifier matches theexecuting-status identifier, the executing-status identifier indicativeof the first node executing during a first logical clock cycle of thedataflow graph; and comparing the node characteristic identifier withthe reference criterion corresponding to a second logical clock cycle ofthe dataflow graph.

In Example 61, the subject matter of any one of Examples 59-60 canoptionally include that the node characteristic identifier is settableto: (a) an unexecuted-status identifier to indicate the first node hasnot yet been executed during execution of the dataflow graph, (b) theexecuting-status identifier, and (c) a completed-status identifier toindicate that no further executions of the first node are to occurduring execution of the dataflow graph.

In Example 62, the subject matter of any one of Examples 59-61 canoptionally include that the node characteristic identifier is a firstdepth level identifier of the first node, the reference criterion is asecond depth level identifier of the second node, and further includeconfirming a presence of the backedge based on execution controlreturning from a higher depth level corresponding to the second depthlevel identifier of the second node to a lower depth level correspondingto the first depth level identifier of the first node.

In Example 63, the subject matter of any one of Examples 59-62 canoptionally include that the coarse-grain reconfigurable architecturedevice includes an array of processing elements interconnected by anetwork, the first node to be executed by a first one of the processingelements, and the second node to be executed by a second one of theprocessing elements.

In Example 64, the subject matter of any one of Examples 59-63 canoptionally include that the storing of the node characteristicidentifier, the comparing of the node characteristic identifier with thereference criterion, and the generating of the backedge identifier areto be performed by a compiler, the compiler to generate the dataflowgraph based on source code in at least one of a high-level programminglanguage or assembly programming language.

In Example 65, the subject matter of any one of Examples 59-64 canoptionally include generating the backedge identifier as a backedgeattribute and to store the backedge attribute in assembly code of thedataflow graph to represent the backedge in the assembly code.

Example 66 is an apparatus to annotate back edges in a dataflow graph.The apparatus of Example 66 includes means for storing a nodecharacteristic identifier in memory in association with a first node ofthe dataflow graph; means for comparing the node characteristicidentifier with a reference criterion; and means for generating abackedge identifier indicative of a backedge between the first node anda second node of the dataflow graph based on the comparison, the memoryto store the backedge identifier in association with a connection arcbetween the first and second nodes.

In Example 67, the subject matter of Example 66 can optionally includethat the reference criterion is an executing-status identifier, and themeans for comparing is to confirm a presence of the backedge between thefirst and second nodes when the node characteristic identifier matchesthe executing-status identifier, the executing-status identifierindicative of the first node executing during a first logical clockcycle of the dataflow graph, and the means for comparing is to comparethe node characteristic identifier with the reference criterioncorresponding to a second logical clock cycle of the dataflow graph.

In Example 68, the subject matter of any one of Examples 66-67 canoptionally include that the node characteristic identifier is settableto: (a) an unexecuted-status identifier to indicate the first node hasnot yet been executed during execution of the dataflow graph, (b) theexecuting-status identifier, and (c) a completed-status identifier toindicate that no further executions of the first node are to occurduring execution of the dataflow graph.

In Example 69, the subject matter of any one of Examples 66-68 canoptionally include that the node characteristic identifier is a firstdepth level identifier of the first node, the reference criterion is asecond depth level identifier of the second node, the means forcomparing is to confirm a presence of the backedge based on executioncontrol returning from a higher depth level corresponding to the seconddepth level identifier of the second node to a lower depth levelcorresponding to the first depth level identifier of the first node.

In Example 70, the subject matter of any one of Examples 66-69 canoptionally include that the coarse-grain reconfigurable architecturedevice includes an array of processing elements interconnected by anetwork, the first node to be executed by a first one of the processingelements, and the second node to be executed by a second one of theprocessing elements.

In Example 71, the subject matter of any one of Examples 66-70 canoptionally include that the means for storing, the means for comparing,and the means for generating the backedge identifier are to operate inassociation with a compiler, the compiler to generate the dataflow graphbased on source code in at least one of a high-level programminglanguage or assembly programming language.

In Example 72, the subject matter of any one of Examples 66-71 canoptionally include that the means for generating the backedge identifieris to generate the backedge identifier as a backedge attribute and tostore the backedge attribute in assembly code of the dataflow graph torepresent the backedge in the assembly code.

Although certain example methods, apparatus and articles of manufacturehave been disclosed herein, the scope of coverage of this patent is notlimited thereto. On the contrary, this patent covers all methods,apparatus and articles of manufacture fairly falling within the scope ofthe claims of this patent.

What is claimed is:
 1. An apparatus comprising: a characteristicdetector to store a node characteristic identifier in memory inassociation with a first node of a dataflow graph; a characteristiccomparator to compare the node characteristic identifier with areference criterion; and a backedge identifier generator to: generate abackedge identifier indicative of a backedge between the first node anda second node of the dataflow graph based on the comparison; and storethe backedge identifier in assembly code of the dataflow graph as abackedge attribute to represent the backedge in the assembly code, thememory to store the backedge identifier in association with a connectionarc between the first and second nodes.
 2. The apparatus of claim 1,wherein the reference criterion is an executing-status identifier, andthe characteristic comparator is to confirm a presence of the backedgebetween the first and second nodes when the node characteristicidentifier matches the executing-status identifier, the executing-statusidentifier indicative of the first node executing during a first logicalclock cycle of the dataflow graph, and the characteristic comparator tocompare the node characteristic identifier with the reference criterioncorresponding to a second logical clock cycle of the dataflow graph. 3.The apparatus of claim 2, wherein the node characteristic identifier issettable to multiple identifiers including at least one of: (a) anunexecuted-status identifier to indicate the first node has not yet beenexecuted during execution of the dataflow graph, (b) theexecuting-status identifier, or (c) a completed-status identifier toindicate that no further executions of the first node are to occurduring execution of the dataflow graph.
 4. The apparatus of claim 1,wherein the node characteristic identifier is a first depth levelidentifier of the first node, the reference criterion is a second depthlevel identifier of the second node, the characteristic comparator is toconfirm a presence of the backedge based on execution control returningfrom a higher depth level corresponding to the second depth levelidentifier of the second node to a lower depth level corresponding tothe first depth level identifier of the first node.
 5. The apparatus ofclaim 1, wherein the first node is to be executed by a first processingelement, and the second node is to be executed by a second processingelement, the first and second processing elements in a coarse-grainreconfigurable architecture device including an array of processingelements interconnected by a network.
 6. The apparatus of claim 1,wherein the characteristic detector, the characteristic comparator, andthe backedge identifier generator are to operate in association with acompiler, the compiler to generate the dataflow graph based on sourcecode in at least one of a high-level programming language or assemblyprogramming language.
 7. A non-transitory computer readable mediumcomprising instructions that, when executed by a processor, cause theprocessor to at least: store a node characteristic identifier in memoryin association with a first node of a dataflow graph; compare the nodecharacteristic identifier with a reference criterion; generate abackedge identifier indicative of a backedge between the first node anda second node of the dataflow graph based on the comparison; and storethe backedge identifier as a backedge attribute in assembly code of thedataflow graph to represent the backedge in the assembly code, thememory to store the backedge identifier in association with a connectionarc between the first and second nodes.
 8. The non-transitory computerreadable medium of claim 7, wherein the reference criterion is anexecuting-status identifier, and the instructions, when executed by theprocessor, are to cause the processor to: confirm a presence of thebackedge between the first and second nodes when the node characteristicidentifier matches the executing-status identifier, the executing-statusidentifier indicative of the first node executing during a first logicalclock cycle of the dataflow graph; and compare the node characteristicidentifier with the reference criterion corresponding to a secondlogical clock cycle of the dataflow graph.
 9. The non-transitorycomputer readable medium of claim 8, wherein the node characteristicidentifier is settable to at least one of: (a) an unexecuted-statusidentifier to indicate the first node has not yet been executed duringexecution of the dataflow graph, (b) the executing-status identifier,and or (c) a completed-status identifier to indicate that no furtherexecutions of the first node are to occur during execution of thedataflow graph.
 10. The non-transitory computer readable medium of claim7, wherein the node characteristic identifier is a first depth levelidentifier of the first node, the reference criterion is a second depthlevel identifier of the second node, the instructions, when executed bythe processor, are to cause the processor to confirm a presence of thebackedge based on execution control returning from a higher depth levelcorresponding to the second depth level identifier of the second node toa lower depth level corresponding to the first depth level identifier ofthe first node.
 11. The non-transitory computer readable medium of claim7, wherein the first node is to be executed by a first processingelement, and the second node is to be executed by a second processingelement.
 12. The non-transitory computer readable medium of claim 7,wherein the instructions are to be executed in association with acompiler, the compiler to generate the dataflow graph based on sourcecode in at least one of a high-level programming language or assemblyprogramming language.
 13. A method comprising: storing a nodecharacteristic identifier in memory in association with a first node ofa dataflow graph; comparing the node characteristic identifier with areference criterion; generating a backedge identifier indicative of abackedge between the first node and a second node of the dataflow graphbased on the comparison; and storing the backedge identifier in assemblycode as a backedge attribute of the dataflow graph to represent thebackedge in the assembly code, the memory to store the backedgeidentifier in association with a connection arc between the first andsecond nodes.
 14. The method of claim 13, wherein the referencecriterion is an executing-status identifier, and the method furtherincluding: confirming a presence of the backedge between the first andsecond nodes when the node characteristic identifier matches theexecuting-status identifier, the executing-status identifier indicativeof the first node executing during a first logical clock cycle of thedataflow graph; and comparing the node characteristic identifier withthe reference criterion corresponding to a second logical clock cycle ofthe dataflow graph.
 15. The method of claim 14, wherein the nodecharacteristic identifier is settable to: (a) an unexecuted-statusidentifier to indicate the first node has not yet been executed duringexecution of the dataflow graph, (b) the executing-status identifier,and (c) a completed-status identifier to indicate that no furtherexecutions of the first node are to occur during execution of thedataflow graph.
 16. The method of claim 13, wherein the nodecharacteristic identifier is a first depth level identifier of the firstnode, the reference criterion is a second depth level identifier of thesecond node, the method further including confirming a presence of thebackedge based on execution control returning from a higher depth levelcorresponding to the second depth level identifier of the second node toa lower depth level corresponding to the first depth level identifier ofthe first node.
 17. The method of claim 13, further including executingthe first node by a first processing element, and executing the secondnode by a second processing element, the first and second processingelements in a coarse-grain reconfigurable architecture device includingan array of processing elements interconnected by a network.
 18. Themethod of claim 13, wherein the storing of the node characteristicidentifier, the comparing of the node characteristic identifier with thereference criterion, and the generating of the backedge identifier areto be performed by a compiler, the compiler to generate the dataflowgraph based on source code in at least one of a high-level programminglanguage or assembly programming language.
 19. An apparatus comprising:means for storing a node characteristic identifier in memory inassociation with a first node of a dataflow graph; means for comparingthe node characteristic identifier with a reference criterion; and meansfor generating a backedge identifier to: generate the backedgeidentifier indicative of a backedge between the first node and a secondnode of the dataflow graph, and store the backedge identifier inassembly code of the dataflow graph as a backedge attribute to representthe backedge in the assembly code, the memory to store the backedgeidentifier in association with a connection arc between the first andsecond nodes.
 20. The apparatus of claim 19, wherein the referencecriterion is an executing-status identifier, and the means for comparingis to confirm a presence of the backedge between the first and secondnodes when the node characteristic identifier matches theexecuting-status identifier, the executing-status identifier indicativeof the first node executing during a first logical clock cycle of thedataflow graph, and the means for comparing is to compare the nodecharacteristic identifier with the reference criterion corresponding toa second logical clock cycle of the dataflow graph.
 21. The apparatus ofclaim 20, wherein the node characteristic identifier is settable tomultiple identifiers including at least one of: (a) an unexecuted-statusidentifier to indicate the first node has not yet been executed duringexecution of the dataflow graph, (b) the executing-status identifier, or(c) a completed-status identifier to indicate that no further executionsof the first node are to occur during execution of the dataflow graph.22. The apparatus of claim 19, wherein the node characteristicidentifier is a first depth level identifier of the first node, thereference criterion is a second depth level identifier of the secondnode, the means for comparing is to confirm a presence of the backedgebased on execution control returning from a higher depth levelcorresponding to the second depth level identifier of the second node toa lower depth level corresponding to the first depth level identifier ofthe first node.
 23. The apparatus of claim 19, wherein the first node isto be executed by a first processing element, and the second node is tobe executed by a second processing element, the first and secondprocessing elements in a coarse-grain reconfigurable architecture deviceincluding an array of processing elements interconnected by a network.24. The apparatus of claim 19, wherein the means for storing, the meansfor comparing, and the means for storing the backedge identifier are tooperate in association with a compiler, the compiler to generate thedataflow graph based on source code in at least one of a high-levelprogramming language or assembly programming language.